Mixed metal dodecaborides and uses thereof

ABSTRACT

Disclosed herein, in certain embodiments, are compounds, methods, tools, and abrasive materials comprising mixed transition metal dodecaborides.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.62/554,376, filed Sep. 5, 2017, which application is incorporated hereinby reference.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with Government support under Grant No. 1506860awarded by the National Science Foundation (NSF). The Government hascertain rights in the invention.

BACKGROUND OF THE INVENTION

In many manufacturing processes, materials must be cut, formed, ordrilled and their surfaces protected with wear-resistant coatings.Diamond has traditionally been the material of choice for theseapplications, due to its superior mechanical properties, e.g.hardness>70 GPa. However, diamond is rare in nature and difficult tosynthesize artificially due to the need for a combination of hightemperature and high pressure conditions. Industrial applications ofdiamond are thus generally limited by cost. Moreover, diamond is not agood option for high-speed cutting of ferrous alloys due to itsgraphitization on the material's surface and formation of brittlecarbides, which leads to poor cutting performance.

SUMMARY OF THE INVENTION

Disclosed herein, in certain embodiments, are composite materials,methods, tools, and abrasive materials comprising mixed metaldodecaborides.

In one embodiment is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;

wherein:

-   -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), or praseodymium (Pr);    -   x is from 0.001 to 0.999.

In one embodiment, is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);

wherein:

-   -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);    -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium        (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),        or lutetium (Lu);    -   x is from 0.001 to 0.999; and    -   c is 12-20; wherein    -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;    -   if A is Y and c is 12, M is not Sc;    -   if A is Sc and c is 12, M is not Y; and    -   A is not M.

In one embodiment, is a method of preparing a composite matrix describedherein, wherein any of Zr, Y, Sc, Gd, Sm, or Nd and B are homogenized inan agate mortar and pestle or a vortex mixer, pressed under an 8-12 tonload, and arc melted under an argon atmosphere. In one embodiment, is amethod of preparing a composite matrix described herein, wherein any ofZr, Y, Sc, Gd, Sm, Nd, Pr, Tb, Dy, Ho, Er, Tm, Yb, or Lu and B arehomogenized in an agate mortar and pestle or a vortex mixer, pressedunder an 8-12 ton load, and arc melted under an argon atmosphere.

In one embodiment, is a lightweight coating comprising a compositedescribed herein.

In one embodiment, is a tool comprising a surface or body for cutting orabrading, wherein the surface or body comprises a composite matrixdescribed herein.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

Various aspects of the invention are set forth with particularity in theappended claims. A better understanding of the features and advantagesof the present invention will be obtained by reference to the followingdetailed description that sets forth illustrative embodiments, in whichthe principles of the invention are utilized, and the accompanyingdrawings of which:

FIG. 1 shows X-ray powder diffractograms of Zr_(1-x)Y_(x)B₁₂.

FIG. 2 shows X-ray powder diffractograms of Zr_(1-x)Sc_(x)B₁₂.

FIG. 3 shows X-ray powder diffractograms of Y_(1-x)Sc_(x)B₁₂.

FIG. 4 shows X-ray powder diffractograms of Zr_(1-x)Gd_(x)B₁₂.

FIG. 5 shows X-ray powder diffractograms of Zr_(1-x)Sm_(x)B₁₂.

FIG. 6 shows X-ray powder diffractograms of Zr_(1-x)Nd_(x)B₁₂.

FIG. 7 shows X-ray powder diffractograms of Zr_(1-x)Pr_(x)B₁₂.

FIG. 8 shows measurements of Vickers microindentation hardness ofZr_(1-x)Y_(x)B₁₂.

FIG. 9 shows measurements of Vickers microindentation hardness ofZr_(1-x)Sc_(x)B₁₂.

FIG. 10 shows measurements of Vickers microindentation hardness ofY_(1-x)Sc_(x)B₁₂.

FIG. 11 shows measurements of Vickers microindentation hardness ofZr_(1-x)Gd_(x)B₁₂.

FIG. 12 shows the thermal stability of Zr_(0.5)Y_(0.5)B₁₂,Zr_(0.5)Sc_(0.5)B₁₂, and Y_(0.5)Sc_(0.5)B₁₂ as measured by thermalgravimetric analysis in air.

FIG. 13 shows the thermal stability of pure Zr_(0.5)Gd_(0.5)B₁₂ andZr_(0.75)Sm_(0.25)B₁₂ as measured by thermal gravimetric analysis inair.

FIG. 14 shows the X-ray powder diffractograms of Zr_(1-x)Y_(x)B₁₂prepared with a metal to boron ratio of 1:13.

FIG. 15 shows the unit cell of the cubic dodecaboride structure type,cubic-UB₁₂ polyhedra model, the unit cell of the tetragonal-ScB₁₂dodecaboride structure type and the tetragonal-ScB₁₂ polyhedra model.

FIG. 16 shows the crystal structure of ScBso and the crystal structureof YB₆₆.

FIG. 17 shows a polyhedra model of the unit cell of a cubic-UB₁₂structural type metal dodecaboride, a polyhedra model of the unit cellof a tetragonal-ScB₁₂ structural type metal dodecaboride, a polyhedramodel of the unit cell of a rhombohedral-MB₅₀ structural type metalboride, and a polyhedra model of the unit cell of a cubic-YB₆₆structural type metal boride.

FIG. 18 shows elemental maps and SEM images of selected samples ofZr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ andZr_(1-x)Pr_(x)B₁₂ alloys.

FIG. 19 shows the SEM images and elemental maps for the hardestcompositions of the mixed metal dodecaborides: Zr_(0.5)Y_(0.5)B₁₂,Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂.

FIG. 20 shows the colors of solid solution samples of the mixed metaldodecaborides Zr_(1-x)Y_(x)B₁₂, Zr_(1-x)Sc_(x)B₁₂, and Y_(1-x)Sc_(x)B₁₂taken using an optical microscope.

FIG. 21 shows the colors of solid solution samples of the mixed metaldodecaborides Zr_(1-x)Gd_(x)B₁₂, and Zr_(1-x)Sm_(x)B₁₂, taken using anoptical microscope.

FIG. 22 shows a transmission electron microscopy image ofZr_(0.05)Sc_(0.95)B₁₂.

FIG. 23 shows the tetragonal diffraction pattern ofZr_(0.05)Sc_(0.95)B₁₂.

FIG. 24 shows powder XRD patterns of ScB₅₀ and YB₆₆.

DETAILED DESCRIPTION OF THE INVENTION

Wear and tear are part of the normal use of tools and machines. Thereare different types of wear mechanisms, including, for example, abrasionwear, adhesion wear, attrition wear, diffusion wear, fatigue wear, edgechipping (or premature wear), and oxidation wear (or corrosive wear).Abrasion wear occurs when the hard particle or debris, such as chips,passes over or abrades the surface of a cutting tool. Adhesion wear orattrition wear occurs when debris removes microscopic fragments from atool. Diffusion wear occurs when atoms in a crystal lattice move from aregion of high concentration to a region of low concentration and themove weakens the surface structure of a tool. Fatigue wear occurs at amicroscopic level when two surfaces slide in contact with each otherunder high pressure, generating surface cracks. Edge chipping orpremature wear occurs as small breaking away of materials from thesurface of a tool. Oxidation wear or corrosive wear occurs as a resultof a chemical reaction between the surface of a tool and oxygen.

The present application discloses new materials having enhancedresistance to the above-mentioned types of wear and tear. Thedevelopment of new materials with superior mechanical properties ischallenging because of the many attributes that need to be controlled,ranging from hardness to oxidation resistance. These new materialformulations may need to be superhard (defined as having Vickershardness (Hv) greater than 40 GPa at a given force of applied load), sothat they may be able to supplant tungsten carbide (Hv=13-25 GPa at 0.5N of applied loading, force comparable to that experienced by materialsduring cutting and machining), the current industrial standard fordrilling and machining, as well as having similar or superior oxidationresistance.

Indeed, the discovery of new superhard materials in higher borides comesfrom attempts to simulate diamond, the hardest material known thus far.Diamond is both highly incompressible and resistant to shear; together,this accounts for diamond's superior resistance to surface deformationand thus, high hardness. Not surprisingly, there are few compounds thatpossess the requisite attributes for superhardness, and among them arethe higher metal borides. For ReB₂, CrB₄ and WB₄, the high electrondensity of the transition metal provides the ultra-incompressibility,while the high density of covalent bonds prevents the propagation ofslip.

Metal dodecaborides (MB₁₂) constitute a class of boron rich compoundspreviously studied for their magnetic, optical and electronicproperties. The structure of all dodecaborides contains boroncuboctahedron cages composed of 24 atoms, each containing a12-coordinate metal in its center. The cages are usually arranged in aface-centered cubic close packed arrangement, forming the cubic-UB₁₂Fm3m structure; however, ScB₁₂ forms its own structuraltype—tetragonal—ScB12 (I4/mmm), where the cuboctahedra are arranged in abody-centered tetragonal close-packed structure. Dodecaborides are knownto exist for a number of metals: transition metals (Zr, Hf, Y and Sc),lanthanides (Tb, Dy, Ho, Er, Tm, Yb and Lu) and actinides (U and Th).For the most part, the aforementioned dodecaborides have been preparedvia arc melting from the elements, or by borothermal reduction of themetal oxide under vacuum, to yield fully dense ingots or compacts,respectively. HfB₁₂ and ThB₁₂ are especially interesting, since in pureform they can only be formed under high pressure (6.5 GPa) and hightemperature (1660° C.); however, they can be stabilized under ambientpressure in the matrices of ZrB₁₂ (Zr_(1-x)Th_(x)B₁₂) and YB₁₂(Y_(1-x)Hf_(x)B₁₂).

The size of a metal atom in a 12-coordinate environment placeslimitations on which atoms can fit inside a boron cuboctahedralenvironment and form a metal dodecaboride. All metal dodecaborides,stable under ambient pressure, have metal atoms with sizes intermediatebetween zirconium (r_(at)=1.55 Å, r_(CN=12)=1.603 Å) and yttrium(r_(at)=1.80 Å, r_(CN=12)=1.801 Å), the smallest and largest metalatoms, respectively, capable of forming a stable transition metaldodecaboride. Therefore, this size requirement results in the stabledodecaboride lattice parameter lying between 7.408 Å (ZrB₁₂) and 7.500 Å(YB₁₂).

Dodecaborides where the metal cation lies outside the range of stability(HfB₁₂, GdB₁₂ and ThB₁₂) requires pressures upwards of 6.5 GPa. Thesephases have metal atoms either smaller than zirconium (Hf, r_(at)=1.55Å, r_(CN=12)=1.580 Å) and thus incapable of accommodating the boroncuboctahedron cage, or larger that yttrium, resulting in a unit cell farexceeding the size of the YB₁₂ cell (a=7.524 Å for GdB₁₂ and a=7.612 Åfor ThB₁₂). The broad applicability of high-pressure synthesis fordodecaborides of all sizes comes from differences in incompressibilitybetween the metal atom and the boron network. For HfB₁₂, hafnium is moreincompressible than the boron network; thus, the boron network shrinksin size under applied pressure, increasing the effective size of thehafnium atom. For GdB₁₂ and ThB₁₂ the effect is reversed, with theeffective size of the metal atom shrinking due to the increasedcompressibility of gadolinium and thorium atoms when compared to theboron network.

Described herein is the stabilization of the high-pressure phase ofGdB₁₂ in a matrix of ZrB₁₂, with a solubility of Gd in ZrB₁₂ reaching 54at. % Gd, along with select properties. Also described are thestabilizations with limited solubilities (below 15%) of previouslyun-synthesized SmB₁₂, NdB₁₂ and PrB₁₂ in ZrB₁₂ matrices, demonstrating adecrease in solubility with increasing size of the secondary metal.

Pure dodecaborides are superhard, which can be attributed to their highisotropy and stiff metal-boron bonds as well as boron-boron bondsforming the cuboctahedra. MB₁₂, as secondary phases, are also known toincrease the hardness of other borides, such as WB4, through extrinsichardening mechanisms. Atomic radii may play a determining role in thedifferent structural types of tetragonal-ScB₁₂ and cubic-MB butelectronic structure of the atoms also plays an important role.Scandium, although being a transition metal, behaves more like analkaline-earth metal.

Apart from the fundamental interest of metal MB₁₂ due to their uniquestructure, their properties are also of interest in industrialapplications, such as Zr-based cutting tools and abrasives (withabrasive qualities comparable to that of diamond, but producing lessroughening of surfaces). Therefore, the mechanical properties(superhardness), lightweight (due to density comparable or lower thanthat of diamond (3.52 g/cm³)) and enhanced oxidation resistanceproperties are of interest for potential applications in machiningindustries and as lightweight protective coatings.

In some embodiments, described herein include composite matrixmaterials, when applied to a tool or abrasive material, reduce the rateof oxidation wear of the tool or abrasive material, or inhibit oxidationwear of the tool or abrasive material. In some embodiments, alsodescribed herein include methods of manufacturing of the compositematrix, and tools and abrasive materials for use with the compositematrix.

In one embodiment is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;

wherein:

-   -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), or praseodymium (Pr);    -   x is from 0.001 to 0.999.

In some embodiments of a composite matrix described herein, x is0.001-0.200. In some embodiments of a composite matrix described herein,x is 0.201-0.400. In some embodiments of a composite matrix describedherein, x is 0.401-0.600. In some embodiments of a composite matrixdescribed herein, x is 0.601-0.800. In some embodiments of a compositematrix described herein, x is 0.801-0.999. In some embodiments of acomposite matrix described herein, x is 0.25. In some embodiments of acomposite matrix described herein, x is 0.50. In some embodiments of acomposite matrix described herein, x is 0.75. In some embodiments of acomposite matrix described herein, x is 0.80. In some embodiments of acomposite matrix described herein, x is 0.85. In some embodiments of acomposite matrix described herein, x is 0.90. In some embodiments of acomposite matrix described herein, x is 0.95. In some embodiments of acomposite matrix described herein, the composite matrix is resistant tooxidation.

In some embodiments of a composite matrix described herein, thecomposite matrix is resistant to oxidation below 620° C. In someembodiments of a composite matrix described herein, the composite matrixis resistant to oxidation below 675° C. In some embodiments of acomposite matrix described herein, the composite matrix is resistant tooxidation below 685° C.

In some embodiments of a composite matrix described herein, thecomposite matrix possesses a density of 4.0 g/cm³ or less. In someembodiments of a composite matrix described herein, the composite matrixpossesses a density of 3.55 g/cm³ or less. In some embodiments of acomposite matrix described herein, the composite matrix possesses adensity of 3.35 g/cm³ or less.

In some embodiments of a composite matrix described herein, thecomposite matrix possesses a density of 3.21 g/cm³ or less. In someembodiments of a composite matrix described herein, the composite matrixpossesses a hardness between 38.0 and 52.0 GPa. In some embodiments of acomposite matrix described herein, the composite matrix possesses ahardness between 44.0 and 48.0 GPa. In some embodiments of a compositematrix described herein, the composite matrix possesses a hardnessbetween 45.0 and 51.0 GPa. In some embodiments of a composite matrixdescribed herein, the composite matrix possesses a hardness between 42.0and 48.0 GPa. In some embodiments of a composite matrix describedherein, the composite matrix possesses a hardness between 38.0 and 45.0GPa.

In some embodiments of a composite matrix described herein, thecomposite matrix unit cell is cubic or tetragonal. In some embodimentsof a composite matrix described herein, the composite matrix unit cellis cubic and the length of a is between 7.350 and 7.550 Å, wherein a isthe length between two adjacent vertices in the unit cell. In someembodiments of a composite matrix described herein, the composite matrixunit cell is tetragonal and the length of a is between 5.150 and 5.450Å, where a is the shortest length between two adjacent vertices in theunit cell, and the length of c is between 7.350 and 7.550 Å, where c isthe longest length between two adjacent vertices in the unit cell.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂. In someembodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂. In someembodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂. In someembodiments, the composite matrix is Zr_(1-x)Gd_(x)B₁₂. In someembodiments, the composite matrix is Zr_(1-x)Sm_(x)B₁₂. In someembodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂. In someembodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ andcharacterized by X-ray diffraction pattern reflections given in Table 8.In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ andcharacterized by at least one X-ray diffraction pattern reflection givenin Table 8. In some embodiments, the composite matrix isZr_(1-x)Sc_(x)B₁₂ and characterized by X-ray diffraction patternreflections given in Tables 9 or 10. In some embodiments, the compositematrix is Zr_(1-x)Sc_(x)B₁₂ and characterized by at least one X-raydiffraction pattern reflection given in Table 9 or 10. In someembodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and characterizedby X-ray diffraction pattern reflections given in Table 11 or 12. Insome embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ andcharacterized by at least one X-ray diffraction pattern reflection givenin Table 11 or 12. In some embodiments, the composite matrix isZr_(1-x)Gd_(x)B₁₂ and characterized by X-ray diffraction patternreflections given in Table 13. In some embodiments, the composite matrixis Zr_(1-x)Gd_(x)B₁₂ and characterized by at least one X-ray diffractionpattern reflection given in Table 13. In some embodiments, the compositematrix is Zr_(1-x)Sm_(x)B₁₂ and characterized by X-ray diffractionpattern reflections given in Table 14. In some embodiments, thecomposite matrix is Zr_(1-x)Sm_(x)B₁₂ and characterized by at least oneX-ray diffraction pattern reflection given in Table 14. In someembodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂ and characterizedby X-ray diffraction pattern reflections given in Table 15. In someembodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂ and characterizedby at least one X-ray diffraction pattern reflection given in Table 15.In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂ andcharacterized by X-ray diffraction pattern reflections given in Table16. In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂ andcharacterized by at least one X-ray diffraction pattern reflection givenin Table 16.

In one embodiment is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);

wherein:

-   -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);    -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium        (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),        or lutetium (Lu);    -   x is from 0.001 to 0.999; and    -   c is 12-20; wherein    -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;    -   if A is Y and c is 12, M is not Sc;    -   if A is Sc and c is 12, M is not Y; and    -   A is not M.

In another embodiment is a method of preparing a composite matrixdescribed herein, wherein the raw materials are homogenized in an agatemortar and pestle or vortex mixer, pressed under an 8-12 ton load, andarc melted under an argon atmosphere. In another embodiment is a methodof preparing a composite matrix described herein, wherein the arcmelting is performed using a current of over 50 A for a time of between0.01 and 5 minutes. In another embodiment is a method of preparing acomposite matrix described herein, wherein the arc melting is performedusing a current of over between 65-75 A for a time of between 1 and 2minutes.

In another embodiment is a lightweight coating comprising a compositematrix described herein.

In another embodiment is a tool comprising a surface or body for cuttingor abrading, wherein the surface or body comprises a composite matrixdescribed herein.

In one embodiment is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;

wherein:

-   -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), or praseodymium (Pr);    -   x is from 0.001 to 0.999.

In one embodiment, the composite matrix is resistant to oxidation. Inone embodiment, the composite matrix possesses a density of 4.0 g/cm³ orless. In one embodiment, the composite matrix possesses a hardnessbetween 38.0 and 52.0 GPa. In one embodiment, the composite matrix iscrystalline. In one embodiment, the composite matrix is crystalline andcomprises a unit cell that is cubic or tetragonal as determined by X-raypowder diffraction. In one embodiment, the unit cell is cubic and thelength between two adjacent vertices in the unit cell is a, and a isfrom 7.350 to 7.550 Å. In one embodiment, the unit cell is tetragonaland comprises two distinct lengths between one vertex and at least twoadjacent vertices, wherein the two distinct lengths comprise a firstlength c and a second length a, wherein c is from 7.350 to 7.550 Å and ais from 5.150 to 5.450 Å. In one embodiment, the composite matrix isZr_(1-x)Y_(x)B₁₂. In one embodiment, the composite matrix isZr_(1-x)Sc_(x)B₁₂. In one embodiment, the composite matrix isY_(1-x)Sc_(x)B₁₂. In one embodiment, the composite matrix isZr_(1-x)Gd_(x)B₁₂. In one embodiment, the composite matrix isZr_(1-x)Sm_(x)B₁₂. In one embodiment, the composite matrix isZr_(1-x)Nd_(x)B₁₂. In one embodiment, the composite matrix isZr_(1-x)Pr_(x)B₁₂.

In one embodiment, is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);

wherein:

-   -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);    -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium        (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),        or lutetium (Lu);    -   x is from 0.001 to 0.999; and    -   c is 12-20; wherein    -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;    -   if A is Y and c is 12, M is not Sc;    -   if A is Sc and c is 12, M is not Y; and    -   A is not M.

In one embodiment, the composite matrix is Y_(1-x)Gd_(x)B_(c),Sc_(1-x)Gd_(x)B_(c), Y_(1-x)Sm_(x)B_(c), Sc_(1-x)Sm_(x)B_(c),Y_(1-x)Nd_(x)B_(c), Sc_(1-x)Nd_(x)B_(c), Y_(1-x)Pr_(x)B_(c),Sc_(1-x)Pr_(x)B_(c), Zr_(1-x)Tb_(x)B_(c), Y_(1-x)Tb_(x)B_(c),Sc_(1-x)Tb_(x)B_(c), Zr_(1-x)Dy_(x)B_(c), Y_(1-x)DY_(x)B_(c),Sc_(1-x)Dy_(x)B_(c), Zr_(1-x)Ho_(x)B_(c), Y_(1-x)Ho_(x)B_(c),Sc_(1-x)Ho_(x)B_(c), Zr_(1-x)Er_(x)B_(c), Y_(1-x)Er_(x)B_(c),Sc_(1-x)Er_(x)B_(c), Zr_(1-x)Tm_(x)B_(c), Y_(1-x)Tm_(x)B_(c),Sc_(1-x)Tm_(x)B_(c), Zr_(1-x)Yb_(x)B_(c), Y_(1-x)Yb_(x)B_(c),Sc_(1-x)Yb_(x)B_(c), Zr_(1-x)Lu_(x)B_(c), Y_(1-x)Lu_(x)B_(c), orSc_(1-x)Lu_(x)B_(c). In one embodiment, is a method of preparing acomposite matrix described herein, wherein any of Zr, Y, Sc, Gd, Sm, orNd and B are homogenized in an agate mortar and pestle or a vortexmixer, pressed under an 8-12 ton load, and arc melted under an argonatmosphere. In one embodiment, is a method of preparing a compositematrix described herein, wherein any of Zr, Y, Sc, Gd, Sm, Nd, Pr, Tb,Dy, Ho, Er, Tm, Yb, or Lu and B are homogenized in an agate mortar andpestle or a vortex mixer, pressed under an 8-12 ton load, and arc meltedunder an argon atmosphere.

In one embodiment, is a lightweight coating comprising a compositedescribed herein.

In one embodiment, is a tool comprising a surface or body for cutting orabrading, wherein the surface or body comprises a composite matrixdescribed herein.

Mixed Metal Dodecaboride Composite Matrix

In some embodiments, a composite matrix described herein comprises acomposition comprising at least two metals and boron (B). In someembodiments, the composite matrix is prepared with a ratio of all metalatoms to boron atoms is about 1 to 12. In some embodiments, thecomposite matrix is a superhard material. In some embodiments, thecomposite matrix comprises a solid solution phase. In some embodiments,the composite matrix is resistant to oxidation.

In some embodiments, a composite matrix described herein comprises acomposition comprising at least two metals and boron (B). In someembodiments, the composite matrix is prepared with a ratio of all metalatoms to boron atoms is from about 1 to 12 to about 1 to 20. In someembodiments, the composite matrix is prepared with a ratio of all metalatoms to boron atoms of about 1 to 12. In some embodiments, thecomposite matrix is prepared with a ratio of all metal atoms to boronatoms of about 1 to 13. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to14. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 15. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 16. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to17. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 18. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 19. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to20.

In one embodiment, described herein is a composite matrix comprising:

-   -   Zr_(1-x)M_(x)B₁₂, or Y_(1-x)Sc_(x)B₁₂;

wherein:

-   -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), or praseodymium (Pr);    -   x is from 0.001 to 0.999.

In some embodiments, M is Y. In some embodiments, M is Sc. In someembodiments, M is Gd. In some embodiments, M is Sm. In some embodiments,M is Nd. In some embodiments, M is Pr.

In some embodiments, M comprises Y, Sc, Gd, Sm, Nd, or Pr. In someembodiments, M comprises Y or Sc. In some embodiments, M comprises Gd,Sm, Nd, or Pr.

In some embodiments, M comprises at least Y. In some embodiments, Mcomprises at least Sc. In some embodiments, M comprises at least Gd. Insome embodiments, M comprises at least Sm. In some embodiments, Mcomprises at least Nd. In some embodiments, M comprises at least Pr. Insome embodiments, M comprises two or more elements selected from Y, Sc,Gd, Sm, Nd, or Pr.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Y_(x)B_(c);

wherein:

-   -   x is from 0.001 to 0.999; and    -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Y_(x)B₁₂;

wherein:

-   -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sc_(1-x)B_(c);

wherein:

-   -   x is from 0.001 to 0.999; and    -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Sc_(1-x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sc_(x)B₁₂;

wherein:

-   -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Y_(1-x)Sc_(x)B_(c);

wherein:

-   -   x is from 0.001 to 0.999; and    -   c is 12-20.

In some embodiments, the composite matrix Y_(1-x)Sc_(1-x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Y_(1-x)Sc_(x)B₁₂;

wherein:

-   -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Gd_(x)B_(c);

wherein:

-   -   x is from 0.001 to 0.999; and    -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Gd_(x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Gd_(x)B₁₂;

wherein:

-   -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Gd_(x)B₁₂ andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sm_(x)B_(c);

wherein:

-   -   x is from 0.001 to 0.999; and    -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Sm_(x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Sm_(x)B₁₂;

wherein:

-   -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Sm_(x)B₁₂ andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Nd_(x)B_(c);

wherein:

-   -   x is from 0.001 to 0.999; and    -   c is 12-20.

In some embodiments, the composite matrix Zr_(1-x)Nd_(x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Nd_(x)B₁₂;

wherein:

-   -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Nd_(x)B₁₂ andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Pr_(x)B_(c);

wherein:

-   -   x is from 0.001 to 0.999; and    -   c is 12-20.

In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments is a composite matrix comprising:

-   -   Zr_(1-x)Pr_(x)B₂;

wherein:

-   -   x is from 0.001 to 0.999.

In some embodiments, the composite matrix is Zr_(1-x)Pr_(x)B₁₂ andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In one embodiment is a composite matrix comprising:

-   -   A_(1-x)M_(x)B_(c);

wherein:

-   -   A is zirconium (Zr), yttrium (Y) or scandium (Sc);    -   M is yttrium (Y), scandium (Sc), gadolinium (Gd), samarium (Sm),        neodymium (Nd), praseodymium (Pr), terbium (Tb), dysprosium        (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb),        or lutetium (Lu);    -   x is from 0.001 to 0.999; and    -   c is 12-20; wherein    -   if A is Zr and c is 12, M is not Y, Sc, Gd, Sm, Nd, or Pr;    -   if A is Y and c is 12, M is not Sc;    -   if A is Sc and c is 12, M is not Y; and    -   A is not M.

In some embodiments, the composite matrix is resistant to oxidation.

In some embodiments, the composite matrix is Y_(1-x)Gd_(x)B_(c),Sc_(1-x)Gd_(x)B_(c), Y_(1-x)Sm_(x)B_(c), Sc_(1-x)Sm_(x)B_(c),Y_(1-x)Nd_(x)B_(c), Sc_(1-x)Nd_(x)B_(c), Y_(1-x)Pr_(x)B_(c),Sc_(1-x)Pr_(x)B_(c), Zr_(1-x)Tb_(x)B_(c), Y_(1-x)Tb_(x)B_(c),Sc_(1-x)Tb_(x)B_(c), Zr_(1-x)Dy_(x)B_(c), Y_(1-x)DY_(x)B_(c),Sc_(1-x)DY_(x)B_(c), Zr_(1-x)Ho_(x)B_(c), Y_(1-x)Ho_(x)B_(c),Sc_(1-x)Ho_(x)B_(c), Zr_(1-x)Er_(x)B_(c), Y_(1-x)Er_(x)B_(c),Sc_(1-x)Er_(x)B_(c), Zr_(1-x)Tm_(x)B_(c), Y_(1-x)Tm_(x)B_(c),Sc_(1-x)Tm_(x)B_(c), Zr_(1-x)Yb_(x)B_(c), Y_(1-x)Yb_(x)B_(c),Sc_(1-x)Yb_(x)B_(c), Zr_(1-x)Lu_(x)B_(c), Y_(1-x)Lu_(x)B_(c), orSc_(1-x)Lu_(x)B_(c).

In some embodiments, the composite matrix is Y_(1-x)Gd_(x)B₁₂,Sc_(1-x)Gd_(x)B₁₂, Y_(1-x)Sm_(x)B₁₂, Sc_(1-x)Sm_(x)B₁₂,Y_(1-x)Nd_(x)B₁₂, Sc_(1-x)Nd_(x)B₁₂, Y_(1-x)Pr_(x)B₁₂,Sc_(1-x)Pr_(x)B₁₂, Zr_(1-x)Tb_(x)B₁₂, Y_(1-x)Tb_(x)B₁₂,Sc_(1-x)Tb_(x)B₁₂, Zr_(1-x)Dy_(x)B₁₂, Y_(1-x)Dy_(x)B₁₂,Sc_(1-x)Dy_(x)B₁₂, Zr_(1-x)Ho_(x)B₁₂, Y_(1-x)Ho_(x)B₁₂,Sc_(1-x)Ho_(x)B₁₂, Zr_(1-x)Er_(x)B₁₂, Y_(1-x)Er_(x)B₁₂,Sc_(1-x)Er_(x)B₁₂, Zr_(1-x)Tm_(x)B₁₂, Y_(1-x)Tm_(x)B₁₂,Sc_(1-x)Tm_(x)B₁₂, Zr_(1-x)Yb_(x)B₁₂, Y_(1-x)Yb_(x)B₁₂,Sc_(1-x)Yb_(x)B₁₂, Zr_(1-x)Lu_(x)B₁₂, Y_(1-x)Lu_(x)B₁₂, orSc_(1-x)Lu_(x)B₁₂.

In some embodiments, the composite matrix is A_(1-x)M_(x)B_(c) andprepared with a ratio of all metal atoms to boron atoms from about 1 to12 to about 1 to 20. In some embodiments, the composite matrix isprepared with a ratio of all metal atoms to boron atoms of about 1 to12. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 13. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 14. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to15. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 16. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 17. In some embodiments, the composite matrixis prepared with a ratio of all metal atoms to boron atoms of about 1 to18. In some embodiments, the composite matrix is prepared with a ratioof all metal atoms to boron atoms of about 1 to 19. In some embodiments,the composite matrix is prepared with a ratio of all metal atoms toboron atoms of about 1 to 20.

In some embodiments, x has a value within the range 0.001 to 0.999,inclusively. In some embodiments, x has a value within the range 0.005to 0.99, 0.01 to 0.95, 0.05 to 0.9, 0.1 to 0.9, 0.001 to 0.6, 0.005 to0.6, 0.01 to 0.6, 0.05 to 0.6, 0.1 to 0.6, 0.2 to 0.6, 0.3 to 0.6, 0.4to 0.6, 0.001 to 0.55, 0.005 to 0.55, 0.01 to 0.55, 0.05 to 0.55, 0.1 to0.55, 0.2 to 0.55, 0.3 to 0.55, 0.4 to 0.55, 0.45 to 0.55, 0.001 to 0.5,0.005 to 0.5, 0.01 to 0.5, 0.05 to 0.5, 0.1 to 0.5, 0.2 to 0.5, 0.3 to0.5, 0.4 to 0.5, 0.5 to 0.55, 0.45 to 0.5, 0.001 to 0.4, 0.005 to 0.4,0.01 to 0.4, 0.05 to 0.4, 0.1 to 0.4, 0.2 to 0.4, 0.001 to 0.3, 0.005 to0.3, 0.01 to 0.3, 0.05 to 0.3, 0.1 to 0.3, 0.001 to 0.2, 0.005 to 0.2,0.01 to 0.2, 0.05 to 0.2, or 0.1 to 0.2, inclusively. In someembodiments, x has a value within the range 0.1 to 0.9, inclusively. Insome embodiments, x has a value within the range 0.001 to 0.6, 0.005 to0.6, 0.001 to 0.4, or 0.001 to 0.2, inclusively. In some embodiments, xhas a value within the range 0.001 to 0.6, inclusively. In someembodiments, x has a value within the range 0.001 to 0.5, inclusively.In some embodiments, x has a value within the range 0.001 to 0.4,inclusively. In some embodiments, x has a value within the range 0.001to 0.3, inclusively. In some embodiments, x has a value within the range0.001 to 0.2, inclusively. In some embodiments, x has a value within therange 0.01 to 0.6, inclusively. In some embodiments, x has a valuewithin the range 0.01 to 0.5, inclusively. In some embodiments, x has avalue within the range 0.01 to 0.4, inclusively. In some embodiments, xhas a value within the range 0.01 to 0.3, inclusively. In someembodiments, x has a value within the range 0.01 to 0.2, inclusively. Insome embodiments, x has a value within the range 0.1 to 0.8,inclusively. In some embodiments, x has a value within the range 0.1 to0.7, inclusively. In some embodiments, x has a value within the range0.1 to 0.6, inclusively. In some embodiments, x has a value within therange 0.1 to 0.5, inclusively. In some embodiments, x has a value withinthe range 0.1 to 0.4, inclusively. In some embodiments, x has a valuewithin the range 0.1 to 0.3, inclusively. In some embodiments, x has avalue within the range 0.1 to 0.2, inclusively. In some embodiments, xhas a value within the range 0.2 to 0.8, inclusively. In someembodiments, x has a value within the range 0.2 to 0.7, inclusively. Insome embodiments, x has a value within the range 0.2 to 0.6,inclusively. In some embodiments, x has a value within the range 0.2 to0.5, inclusively. In some embodiments, x has a value within the range0.2 to 0.4, inclusively. In some embodiments, x has a value within therange 0.2 to 0.3, inclusively. In some embodiments, x has a value withinthe range 0.3 to 0.8, inclusively. In some embodiments, x has a valuewithin the range 0.3 to 0.7, inclusively. In some embodiments, x has avalue within the range 0.3 to 0.6, inclusively. In some embodiments, xhas a value within the range 0.3 to 0.5, inclusively. In someembodiments, x has a value within the range 0.3 to 0.4, inclusively. Insome embodiments, x has a value within the range 0.4 to 0.8,inclusively. In some embodiments, x has a value within the range 0.4 to0.7, inclusively. In some embodiments, x has a value within the range0.4 to 0.6, inclusively. In some embodiments, x has a value within therange 0.4 to 0.5, inclusively.

In some embodiments, x is at least 0.001 and less than 0.999. In someembodiments, x is at least 0.001 and less than 0.9. In some embodiments,x is at least 0.001 and less than 0.6. In some embodiments, x is atleast 0.001 and less than 0.5. In some embodiments, x is at least 0.001and less than 0.4. In some embodiments, x is at least 0.001 and lessthan 0.3. In some embodiments, x is at least 0.001 and less than 0.2. Insome embodiments, x is at least 0.001 and less than 0.05. In someembodiments, x is at least 0.01 and less than 0.5. In some embodiments,x is at least 0.01 and less than 0.4. In some embodiments, x is at least0.01 and less than 0.3. In some embodiments, x is at least 0.01 and lessthan 0.2. In some embodiments, x is at least 0.1 and less than 0.5. Insome embodiments, x is at least 0.1 and less than 0.4. In someembodiments, x is at least 0.1 and less than 0.3. In some embodiments, xis at least 0.1 and less than 0.2.

In some embodiments, x has a value of about 0.001, 0.005, 0.01, 0.05,0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45,0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57,0.58, 0.59, 0.6, 0.65, 0.7, 0.8, 0.9, 0.95, 0.99, or about 0.999. Insome embodiments, x has a value of about 0.001. In some embodiments, xhas a value of about 0.005. In some embodiments, x has a value of about0.01. In some embodiments, x has a value of about 0.05. In someembodiments, x has a value of about 0.1. In some embodiments, x has avalue of about 0.15. In some embodiments, x has a value of about 0.2. Insome embodiments, x has a value of about 0.3. In some embodiments, x hasa value of about 0.4. In some embodiments, x has a value of about 0.41.In some embodiments, x has a value of about 0.42. In some embodiments, xhas a value of about 0.43. In some embodiments, x has a value of about0.44. In some embodiments, x has a value of about 0.45. In someembodiments, x has a value of about 0.46. In some embodiments, x has avalue of about 0.47. In some embodiments, x has a value of about 0.48.In some embodiments, x has a value of about 0.49. In some embodiments, xhas a value of about 0.5. In some embodiments, x has a value of about0.51. In some embodiments, x has a value of about 0.52. In someembodiments, x has a value of about 0.53. In some embodiments, x has avalue of about 0.54. In some embodiments, x has a value of about 0.55.In some embodiments, x has a value of about 0.56. In some embodiments, xhas a value of about 0.57. In some embodiments, x has a value of about0.58. In some embodiments, x has a value of about 0.59. In someembodiments, x has a value of about 0.6. In some embodiments, x has avalue of about 0.7. In some embodiments, x has a value of about 0.8. Insome embodiments, x has a value of about 0.9. In some embodiments, x hasa value of about 0.99.

In some embodiments, x is 0.001-0.200. In some embodiments, x is0.201-0.400. In some embodiments, x is 0.401-0.600. In some embodiments,x is 0.601-0.800. In some embodiments, x is 0.801-0.999.

In some embodiments, x is about 0.05. In some embodiments, x is about0.25. In some embodiments, x is about 0.50. In some embodiments, x isabout 0.75. In some embodiments, x is about 0.80. In some embodiments, xis about 0.85. In some embodiments, x is about 0.90. In someembodiments, x is about 0.95.

In some embodiments, c has a value of 12-20. In some embodiments, c hasa value of 12. In some embodiments, c has a value of 13. In someembodiments, c has a value of 14. In some embodiments, c has a value of15. In some embodiments, c has a value of 16. In some embodiments, c hasa value of 17. In some embodiments, c has a value of 18. In someembodiments, c has a value of 19. In some embodiments, c has a value of20. In some embodiments, c has a value within the range of 12-13. Insome embodiments, c has a value within the range of 13-14. In someembodiments, c has a value within the range of 14-15. In someembodiments, c has a value within the range of 15-16. In someembodiments, c has a value within the range of 17-18. In someembodiments, c has a value within the range of 19-20. In someembodiments, c has a value within the range of 12-14. In someembodiments, c has a value within the range of 12-16. In someembodiments, c has a value within the range of 12-18. In someembodiments, c has a value within the range of 14-16. In someembodiments, c has a value within the range of 14-18. In someembodiments, c has a value within the range of 14-20. In someembodiments, c has a value within the range of 16-18. In someembodiments, c has a value within the range of 16-20. In someembodiments, c has a value within the range of 18-20.

In some embodiments M is Y, and x is at least 0.001 and less than 0.999.In some embodiments M is Y, and x is at least 0.100 and less than 0.900.In some embodiments M is Y, and x is at least 0.200 and less than 0.800.In some embodiments M is Y, and x is at least 0.300 and less than 0.700.In some embodiments M is Y, and x is at least 0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Y_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Y_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Y_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Y_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Y_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Y_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Y_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Y_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Y_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Y_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Y_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Y_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Y_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Y_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Y_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Y_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Y_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Y_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Y_(0.95)B₁₂.

In some embodiments M is Sc, and x is at least 0.001 and less than0.999. In some embodiments M is Sc, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Sc, and x is at least 0.200 andless than 0.800. In some embodiments M is Sc, and x is at least 0.300and less than 0.700. In some embodiments M is Sc, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Sc_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90) Sc_(0.10)B₁₂. Insome embodiments, the composite matrix is Zr_(0.85)Sc_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Sc_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Sc_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Sc_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Sc_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Sc_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Sc_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Sc_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Sc_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Sc_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Sc_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Sc_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Sc_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Sc_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Sc_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Sc_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05) Sc_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Sc_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Sc_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Sc_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Sc_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Sc_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Sc_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Sc_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Sc_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Sc_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Sc_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Sc_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Sc_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Sc_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Sc_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Sc_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Sc_(0.80)B₁₂. In someembodiments, the composite matrix is Y_(0.15)Sc_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Sc_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Sc_(0.95)B₁₂.

In some embodiments M is Gd, and x is at least 0.001 and less than0.999. In some embodiments M is Gd, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Gd, and x is at least 0.200 andless than 0.800. In some embodiments M is Gd, and x is at least 0.300and less than 0.700. In some embodiments M is Gd, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Gd_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Gd_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Gd_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Gd_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Gd_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Gd_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65) Gd_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Gd_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Gd_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Gd_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Gd_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Gd_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35) Gd_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Gd_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25) Gd_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Gd_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Gd_(0.0312). In someembodiments, the composite matrix is Zr_(0.10)Gd_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Gd_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Gd_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Gd_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Gd_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Gd_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Gd_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Gd_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65) Gd_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Gd_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Gd_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Gd_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Gd_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Gd_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Gd_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Gd_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Gd_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Gd_(0.0312). In someembodiments, the composite matrix is Y_(0.15)Gd_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Gd_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Gd_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Gd_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Gd_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Gd_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Gd_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Gd_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Gd_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65) Gd_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Gd_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Gd_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Gd_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Gd_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Gd_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35) Gd_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Gd_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Gd_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Gd_(0.80)B₁₂. In someembodiments, the composite matrix is Sc_(0.15)Gd_(0.0312). In someembodiments, the composite matrix is Sc_(0.10)Gd_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Gd_(0.95)B₁₂.

In some embodiments M is Sm, and x is at least 0.001 and less than0.999. In some embodiments M is Sm, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Sm, and x is at least 0.200 andless than 0.800. In some embodiments M is Sm, and x is at least 0.300and less than 0.700. In some embodiments M is Sm, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Sm_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Sm_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Sm_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Sm_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Sm_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Sm_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Sm_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Sm_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Sm_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Sm_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Sm_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Sm_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Sm_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Sm_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Sm_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Sm_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Sm_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Sm_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Sm_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Sm_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Sm_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Sm_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Sm_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Sm_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Sm_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Sm_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Sm_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Sm_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Sm_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Sm_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Sm_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Sm_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Sm_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Sm_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Sm_(0.80)B₁₂. In someembodiments, the composite matrix is Y_(0.15)Sm_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Sm_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Sm_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Sm_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Sm_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Sm_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Sm_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Sm_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Sm_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Sm_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Sm_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Sm_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Sm_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Sm_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Sm_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Sm_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Sm_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Sm_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Sm_(0.80)B₁₂. In someembodiments, the composite matrix is Sc_(0.15)Sm_(0.85)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Sm_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Sm_(0.95)B₁₂.

In some embodiments M is Nd, and x is at least 0.001 and less than0.999. In some embodiments M is Nd, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Nd, and x is at least 0.200 andless than 0.800. In some embodiments M is Nd, and x is at least 0.300and less than 0.700. In some embodiments M is Nd, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Nd_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Nd_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Nd_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Nd_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Nd_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Nd_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65) Nd_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Nd_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55) Nd_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Nd_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45) Nd_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40) Nd_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35) Nd_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Nd_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25) Nd_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Nd_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15) Nd_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Nd_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05) Nd_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Nd_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Nd_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Nd_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Nd_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Nd_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Nd_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Nd_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Nd_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55) Nd_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Nd_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45) Nd_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40) Nd_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Nd_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30) Nd_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25) Nd_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Nd_(0.0312). In someembodiments, the composite matrix is Y_(0.15) Nd_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Nd_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Nd_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Nd_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90) Nd_(0.10)B₁₂. Insome embodiments, the composite matrix is Sc_(0.85)Nd_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Nd_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Nd_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Nd_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65) Nd_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Nd_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Nd_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Nd_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Nd_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Nd_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35) Nd_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Nd_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Nd_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Nd_(0.80)B₁₂. In someembodiments, the composite matrix is Sc_(0.15)Nd_(0.85)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Nd_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Nd_(0.95)B₁₂.

In some embodiments M is Pr, and x is at least 0.001 and less than0.999. In some embodiments M is Pr, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Pr, and x is at least 0.200 andless than 0.800. In some embodiments M is Pr, and x is at least 0.300and less than 0.700. In some embodiments M is Pr, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Pr_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Pr_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Pr_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Pr_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Pr_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Pr_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Pr_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Pr_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Pr_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Pr_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Pr_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Pr_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Pr_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Pr_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Pr_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Pr_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Pr_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Pr_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Pr_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Pr_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Pr_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Pr_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Pr_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Pr_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Pr_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Pr_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Pr_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Pr_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Pr_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Pr_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Pr_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Pr_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Pr_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Pr_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Pr_(0.80)B₁₂. In someembodiments, the composite matrix is Y_(0.15)Pr_(0.03)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Pr_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Pr_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Pr_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Pr_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Pr_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Pr_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Pr_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Pr_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Pr_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Pr_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Pr_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Pr_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Pr_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Pr_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Pr_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Pr_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Pr_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Pr_(0.0312). In someembodiments, the composite matrix is Sc_(0.15)Pr_(0.85)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Pr_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Pr_(0.95)B₁₂.

In some embodiments, the composite matrix is Zr_(1-x)Tb_(x)B₁₂,Y_(1-x)Tb_(x)B₁₂, Sc_(1-x)Tb_(x)B₁₂, Zr_(1-x)Dy_(x)B₁₂,Y_(1-x)Dy_(x)B₁₂, Sc_(1-x)Dy_(x)B₁₂, Zr_(1-x)Ho_(x)B₁₂,Y_(1-x)Ho_(x)B₁₂, Sc_(1-x)Ho_(x)B₁₂, Zr_(1-x)Er_(x)B₁₂,Y_(1-x)Er_(x)B₁₂, Sc_(1-x)Er_(x)B₁₂, Zr_(1-x)Tm_(x)B₁₂,Y_(1-x)Tm_(x)B₁₂, Sc_(1-x)Tm_(x)B₁₂, Zr_(1-x)Yb_(x)B₁₂,Y_(1-x)Yb_(x)B₁₂, Sc_(1-x)Yb_(x)B₁₂, Zr_(1-x)Lu_(x)B₁₂,Y_(1-x)Lu_(x)B₁₂, or Sc_(1-x)Lu_(x)B₁₂.

In some embodiments M is Tb, and x is at least 0.001 and less than0.999. In some embodiments M is Tb, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Tb, and x is at least 0.200 andless than 0.800. In some embodiments M is Tb, and x is at least 0.300and less than 0.700. In some embodiments M is Tb, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Tb_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Tb_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Tb_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Tb_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Tb_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Tb_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Tb_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Tb_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Tb_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Tb_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Tb_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Tb_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Tb_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Tb_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Tb_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Tb_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Tb_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Tb_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Tb_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Tb_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Tb_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Tb_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Tb_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Tb_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Tb_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Tb_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Tb_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Tb_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Tb_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Tb_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Tb_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Tb_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Tb_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Tb_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Tb_(0.80)B₁₂. In someembodiments, the composite matrix is Y_(0.15)Tb_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Tb_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Tb_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Tb_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Tb_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Tb_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Tb_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Tb_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Tb_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Tb_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Tb_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Tb_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Tb_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Tb_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Tb_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Tb_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Tb_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Tb_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Tb_(0.0312). In someembodiments, the composite matrix is Sc_(0.15)Tb_(0.85)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Tb_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Tb_(0.95)B₁₂.

In some embodiments M is Dy, and x is at least 0.001 and less than0.999. In some embodiments M is Dy, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Dy, and x is at least 0.200 andless than 0.800. In some embodiments M is Dy, and x is at least 0.300and less than 0.700. In some embodiments M is Dy, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Dy_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Dy_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Dy_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Dy_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Dy_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Dy_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Dy_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Dy_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Dy_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Dy_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Dy_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Dy_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Dy_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Dy_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Dy_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Dy_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Dy_(0.0312). In someembodiments, the composite matrix is Zr_(0.10)Dy_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Dy_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Dy_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Dy_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Dy_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Dy_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Dy_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Dy_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Dy_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Dy_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Dy_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Dy_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Dy_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Dy_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Dy_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Dy_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Dy_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Dy_(0.0312). In someembodiments, the composite matrix is Y_(0.15)Dy_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Dy_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Dy_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Dy_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Dy_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Dy_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Dy_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Dy_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Dy_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Dy_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Dy_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Dy_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Dy_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Dy_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Dy_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Dy_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Dy_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Dy_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Dy_(0.0312). In someembodiments, the composite matrix is Sc_(0.15)Dy_(0.03)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Dy_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Dy_(0.95)B₁₂.

In some embodiments M is Ho, and x is at least 0.001 and less than0.999. In some embodiments M is Ho, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Ho, and x is at least 0.200 andless than 0.800. In some embodiments M is Ho, and x is at least 0.300and less than 0.700. In some embodiments M is Ho, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Ho_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Ho_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Ho_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Ho_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Ho_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Ho_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Ho_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Ho_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Ho_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Ho_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Ho_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Ho_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Ho_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Ho_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Ho_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Ho_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Ho_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Ho_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Ho_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Ho_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Ho_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Ho_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Ho_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Ho_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Ho_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Ho_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Ho_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Ho_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Ho_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Ho_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Ho_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Ho_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Ho_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Ho_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Ho_(0.0312). In someembodiments, the composite matrix is Y_(0.15)Ho_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Ho_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Ho_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Ho_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Ho_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Ho_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Ho_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Ho_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Ho_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Ho_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Ho_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Ho_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Ho_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Ho_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Ho_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Ho_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Ho_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Ho_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Ho_(0.80)B₁₂. In someembodiments, the composite matrix is Sc_(0.15)Ho_(0.0312). In someembodiments, the composite matrix is Sc_(0.10)Ho_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Ho_(0.95)B₁₂.

In some embodiments M is Er, and x is at least 0.001 and less than0.999. In some embodiments M is Er, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Er, and x is at least 0.200 andless than 0.800. In some embodiments M is Er, and x is at least 0.300and less than 0.700. In some embodiments M is Er, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Er_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Er_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Er_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Er_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Er_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Er_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Er_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Er_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Er_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Er_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Er_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Er_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Er_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Er_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Er_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Er_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Er_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Er_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Er_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Er_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Er_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Er_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Er_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Er_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Er_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Er_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Er_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Er_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Er_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Er_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Er_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Er_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Er_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Er_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Er_(0.80)B₁₂. In someembodiments, the composite matrix is Y_(0.15)Er_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Er_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Er_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Er_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Er_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Er_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Er_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Er_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Er_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Er_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Er_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Er_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Er_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Er_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Er_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Er_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Er_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Er_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Er_(0.0312). In someembodiments, the composite matrix is Sc_(0.15)Er_(0.85)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Er_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Er_(0.95)B₁₂.

In some embodiments M is Tm, and x is at least 0.001 and less than0.999. In some embodiments M is Tm, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Tm, and x is at least 0.200 andless than 0.800. In some embodiments M is Tm, and x is at least 0.300and less than 0.700. In some embodiments M is Tm, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Tm_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Tm_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Tm_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Tm_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75) Tm_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Tm_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Tm_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Tm_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Tm_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Tm_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45) Tm_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Tm_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Tm_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Tm_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Tm_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Tm_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Tm_(0.0312). In someembodiments, the composite matrix is Zr_(0.10)Tm_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Tm_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Tm_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Tm_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Tm_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Tm_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75) Tm_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Tm_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Tm_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60) Tm_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Tm_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Tm_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45) Tm_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40) Tm_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Tm_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30) Tm_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Tm_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Tm_(0.80)B₁₂. In someembodiments, the composite matrix is Y_(0.15)Tm_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Tm_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Tm_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Tm_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Tm_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Tm_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Tm_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Tm_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Tm_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Tm_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Tm_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Tm_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Tm_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Tm_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Tm_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Tm_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Tm_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Tm_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Tm_(0.0312). In someembodiments, the composite matrix is Sc_(0.15)Tm_(0.85)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Tm_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Tm_(0.95)B₁₂.

In some embodiments M is Yb, and x is at least 0.001 and less than0.999. In some embodiments M is Yb, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Yb, and x is at least 0.200 andless than 0.800. In some embodiments M is Yb, and x is at least 0.300and less than 0.700. In some embodiments M is Yb, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Yb_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Yb_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Yb_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Yb_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Yb_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Yb_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Yb_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Yb_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Yb_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Yb_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Yb_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Yb_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Yb_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Yb_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Yb_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Yb_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Yb_(0.0312). In someembodiments, the composite matrix is Zr_(0.10)Yb_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Yb_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Yb_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Yb_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Yb_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Yb_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Yb_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Yb_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Yb_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Yb_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Yb_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Yb_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Yb_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Yb_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Yb_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Yb_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Yb_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Yb_(0.0312). In someembodiments, the composite matrix is Y_(0.15)Yb_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Yb_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Yb_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Yb_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Yb_(0.10)B₂. In someembodiments, the composite matrix is Sc_(0.85)Yb_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Yb_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Yb_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Yb_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Yb_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Yb_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Yb_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Yb_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Yb_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Yb_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Yb_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Yb_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Yb_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Yb_(0.80)B₁₂. In someembodiments, the composite matrix is Sc_(0.15)Yb_(0.0312). In someembodiments, the composite matrix is Sc_(0.10)Yb_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Yb_(0.95)B₁₂.

In some embodiments M is Lu, and x is at least 0.001 and less than0.999. In some embodiments M is Lu, and x is at least 0.100 and lessthan 0.900. In some embodiments M is Lu, and x is at least 0.200 andless than 0.800. In some embodiments M is Lu, and x is at least 0.300and less than 0.700. In some embodiments M is Lu, and x is at least0.400 and less than 0.600.

In some embodiments, the composite matrix is Zr_(0.95)Lu_(0.05)B₁₂. Insome embodiments, the composite matrix is Zr_(0.90)Lu_(0.10)B₁₂. In someembodiments, the composite matrix is Zr_(0.85)Lu_(0.15)B₁₂. In someembodiments, the composite matrix is Zr_(0.80)Lu_(0.20)B₁₂. In someembodiments, the composite matrix is Zr_(0.75)Lu_(0.25)B₁₂. In someembodiments, the composite matrix is Zr_(0.70)Lu_(0.30)B₁₂. In someembodiments, the composite matrix is Zr_(0.65)Lu_(0.35)B₁₂. In someembodiments, the composite matrix is Zr_(0.60)Lu_(0.40)B₁₂. In someembodiments, the composite matrix is Zr_(0.55)Lu_(0.45)B₁₂. In someembodiments, the composite matrix is Zr_(0.50)Lu_(0.50)B₁₂. In someembodiments, the composite matrix is Zr_(0.45)Lu_(0.55)B₁₂. In someembodiments, the composite matrix is Zr_(0.40)Lu_(0.60)B₁₂. In someembodiments, the composite matrix is Zr_(0.35)Lu_(0.65)B₁₂. In someembodiments, the composite matrix is Zr_(0.30)Lu_(0.70)B₁₂. In someembodiments, the composite matrix is Zr_(0.25)Lu_(0.75)B₁₂. In someembodiments, the composite matrix is Zr_(0.20)Lu_(0.80)B₁₂. In someembodiments, the composite matrix is Zr_(0.15)Lu_(0.85)B₁₂. In someembodiments, the composite matrix is Zr_(0.10)Lu_(0.90)B₁₂. In someembodiments, the composite matrix is Zr_(0.05)Lu_(0.95)B₁₂.

In some embodiments, the composite matrix is Y_(0.95)Lu_(0.05)B₁₂. Insome embodiments, the composite matrix is Y_(0.90)Lu_(0.10)B₁₂. In someembodiments, the composite matrix is Y_(0.85)Lu_(0.15)B₁₂. In someembodiments, the composite matrix is Y_(0.80)Lu_(0.20)B₁₂. In someembodiments, the composite matrix is Y_(0.75)Lu_(0.25)B₁₂. In someembodiments, the composite matrix is Y_(0.70)Lu_(0.30)B₁₂. In someembodiments, the composite matrix is Y_(0.65)Lu_(0.35)B₁₂. In someembodiments, the composite matrix is Y_(0.60)Lu_(0.40)B₁₂. In someembodiments, the composite matrix is Y_(0.55)Lu_(0.45)B₁₂. In someembodiments, the composite matrix is Y_(0.50)Lu_(0.50)B₁₂. In someembodiments, the composite matrix is Y_(0.45)Lu_(0.55)B₁₂. In someembodiments, the composite matrix is Y_(0.40)Lu_(0.60)B₁₂. In someembodiments, the composite matrix is Y_(0.35)Lu_(0.65)B₁₂. In someembodiments, the composite matrix is Y_(0.30)Lu_(0.70)B₁₂. In someembodiments, the composite matrix is Y_(0.25)Lu_(0.75)B₁₂. In someembodiments, the composite matrix is Y_(0.20)Lu_(0.80)B₁₂. In someembodiments, the composite matrix is Y_(0.15)Lu_(0.85)B₁₂. In someembodiments, the composite matrix is Y_(0.10)Lu_(0.90)B₁₂. In someembodiments, the composite matrix is Y_(0.05)Lu_(0.95)B₁₂.

In some embodiments, the composite matrix is Sc_(0.95)Lu_(0.05)B₁₂. Insome embodiments, the composite matrix is Sc_(0.90)Lu_(0.10)B₁₂. In someembodiments, the composite matrix is Sc_(0.85)Lu_(0.15)B₁₂. In someembodiments, the composite matrix is Sc_(0.80)Lu_(0.20)B₁₂. In someembodiments, the composite matrix is Sc_(0.75)Lu_(0.25)B₁₂. In someembodiments, the composite matrix is Sc_(0.70)Lu_(0.30)B₁₂. In someembodiments, the composite matrix is Sc_(0.65)Lu_(0.35)B₁₂. In someembodiments, the composite matrix is Sc_(0.60)Lu_(0.40)B₁₂. In someembodiments, the composite matrix is Sc_(0.55)Lu_(0.45)B₁₂. In someembodiments, the composite matrix is Sc_(0.50)Lu_(0.50)B₁₂. In someembodiments, the composite matrix is Sc_(0.45)Lu_(0.55)B₁₂. In someembodiments, the composite matrix is Sc_(0.40)Lu_(0.60)B₁₂. In someembodiments, the composite matrix is Sc_(0.35)Lu_(0.65)B₁₂. In someembodiments, the composite matrix is Sc_(0.30)Lu_(0.70)B₁₂. In someembodiments, the composite matrix is Sc_(0.25)Lu_(0.75)B₁₂. In someembodiments, the composite matrix is Sc_(0.20)Lu_(0.80)B₁₂. In someembodiments, the composite matrix is Sc_(0.15)Lu_(0.85)B₁₂. In someembodiments, the composite matrix is Sc_(0.10)Lu_(0.90)B₁₂. In someembodiments, the composite matrix is Sc_(0.05)Lu_(0.95)B₁₂.

In some embodiments, the hardness described herein is measured by aVickers hardness test. In some embodiments, the hardness is measuredunder a load of 0.49 Newton (N).

In some embodiments, a composite matrix described herein has a hardnessof about 10 to about 70 GPa. In some embodiments, a composite matrixdescribed herein has a hardness of about 10 to about 60 GPa, about 10 toabout 50 GPa, about 10 to about 40 GPa, about 10 to about 30 GPa, about20 to about 70 GPa, about 20 to about 60 GPa, about 20 to about 50 GPa,about 20 to about 40 GPa, about 20 to about 30 GPa, about 30 to about 70GPa, about 30 to about 60 GPa, about 30 to about 50 GPa, about 30 toabout 45 GPa, about 30 to about 40 GPa, about 30 to about 35 GPa, about35 to about 70 GPa, about 35 to about 60 GPa, about 35 to about 50 GPa,about 35 to about 40 GPa, about 40 to about 70 GPa, about 40 to about 60GPa, about 40 to about 50 GPa, about 45 to about 60 GPa or about 45 toabout 50 GPa. In some embodiments, a composite matrix described hereinhas a hardness of about 30 to about 50 GPa, about 30 to about 45 GPa,about 30 to about 40 GPa, about 30 to about 35 GPa, about 35 to about 50GPa, about 35 to about 40 GPa, about 40 to about 50 GPa, or about 45 toabout 50 GPa.

In some embodiments, a composite matrix described herein has a hardnessof about 10 GPa, about 15 GPa, about 20 GPa, about 25 GPa, about 30 GPa,about 31 GPa, about 32 GPa, about 33 GPa, about 34 GPa, about 35 GPa,about 36 GPa, about 37 GPa, about 38 GPa, about 39 GPa, about 40 GPa,about 41 GPa, about 42 GPa, about 43 GPa, about 44 GPa, about 45 GPa,about 46 GPa, about 47 GPa, about 48 GPa, about 49 GPa, about 50 GPa,about 51 GPa, about 52 GPa, about 53 GPa, about 54 GPa, about 55 GPa,about 56 GPa, about 57 GPa, about 58 GPa, about 59 GPa, about 60 GPa orhigher. In some embodiments, a composite matrix described herein has ahardness of about 10 GPa or higher. In some embodiments, a compositematrix described herein has a hardness of about 15 GPa or higher. Insome embodiments, a composite matrix described herein has a hardness ofabout 20 GPa or higher. In some embodiments, a composite matrixdescribed herein has a hardness of about 25 GPa or higher. In someembodiments, a composite matrix described herein has a hardness of about30 GPa or higher. In some embodiments, a composite matrix describedherein has a hardness of about 31 GPa or higher. In some embodiments, acomposite matrix described herein has a hardness of about 32 GPa orhigher. In some embodiments, a composite matrix described herein has ahardness of about 33 GPa or higher. In some embodiments, a compositematrix described herein has a hardness of about 34 GPa or higher. Insome embodiments, a composite matrix described herein has a hardness ofabout 35 GPa or higher. In some embodiments, a composite matrixdescribed herein has a hardness of about 36 GPa or higher. In someembodiments, a composite matrix described herein has a hardness of about37 GPa or higher. In some embodiments, a composite matrix describedherein has a hardness of about 38 GPa or higher. In some embodiments, acomposite matrix described herein has a hardness of about 39 GPa orhigher. In some embodiments, a composite matrix described herein has ahardness of about 40 GPa or higher. In some embodiments, a compositematrix described herein has a hardness of about 41 GPa or higher. Insome embodiments, a composite matrix described herein has a hardness ofabout 42 GPa or higher. In some embodiments, a composite matrixdescribed herein has a hardness of about 43 GPa or higher. In someembodiments, a composite matrix described herein has a hardness of about44 GPa or higher. In some embodiments, a composite matrix describedherein has a hardness of about 45 GPa or higher. In some embodiments, acomposite matrix described herein has a hardness of about 46 GPa orhigher. In some embodiments, a composite matrix described herein has ahardness of about 47 GPa or higher. In some embodiments, a compositematrix described herein has a hardness of about 48 GPa or higher. Insome embodiments, a composite matrix described herein has a hardness ofabout 49 GPa or higher. In some embodiments, a composite matrixdescribed herein has a hardness of about 50 GPa or higher. In someembodiments, a composite matrix described herein has a hardness of about51 GPa or higher. In some embodiments, a composite matrix describedherein has a hardness of about 52 GPa or higher. In some embodiments, acomposite matrix described herein has a hardness of about 53 GPa orhigher. In some embodiments, a composite matrix described herein has ahardness of about 54 GPa or higher. In some embodiments, a compositematrix described herein has a hardness of about 55 GPa or higher. Insome embodiments, a composite matrix described herein has a hardness ofabout 56 GPa or higher. In some embodiments, a composite matrixdescribed herein has a hardness of about 57 GPa or higher. In someembodiments, a composite matrix described herein has a hardness of about58 GPa or higher. In some embodiments, a composite matrix describedherein has a hardness of about 59 GPa or higher. In some embodiments, acomposite matrix described herein has a hardness of about 60 GPa orhigher.

In some embodiments, a composite matrix described herein has a hardnessbetween 38.0 and 52.0 GPa.

In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has ahardness between 38.0 and 52.0 GPa. In some embodiments, a compositematrix is Zr_(1-x)Y_(x)B₁₂ and has a hardness between 40.0 and 50.0 GPa.In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has ahardness between 42.0 and 48.0 GPa. In some embodiments, a compositematrix is Zr_(1-x)Y_(x)B₁₂ and has a hardness between 44.0 and 48.0 GPa.In some embodiments, a composite matrix is Zr_(1-x)Y_(x)B₁₂ and has ahardness between 45.0 and 46.0 GPa.

In some embodiments, a composite matrix is Zr_(1-x)Sc_(x)B₁₂ and has ahardness between 38.0 and 52.0 GPa. In some embodiments, a compositematrix is Zr_(1-x)Sc_(x)B₁₂ and has a hardness between 45.0 and 51.0GPa. In some embodiments, a composite matrix is Zr_(1-x)Sc_(x)B₁₂ andhas a hardness between 46.0 and 50.0 GPa. In some embodiments, acomposite matrix is Zr_(1-x)Sc_(x)B₁₂ and has a hardness between 47.0and 49.0 GPa.

In some embodiments, a composite matrix is Y_(1-x)Sc_(x)B₁₂ and has ahardness between 38.0 and 52.0 GPa. In some embodiments, a compositematrix is Y_(1-x)Sc_(x)B₁₂ and has a hardness between 40.0 and 50.0 GPa.In some embodiments, a composite matrix is Y_(1-x)Sc_(x)B₁₂ and has ahardness between 42.0 and 48.0 GPa. In some embodiments, a compositematrix is Y_(1-x)Sc_(x)B₁₂ and has a hardness between 44.0 and 46.0 GPa.

In some embodiments, a composite matrix is Zr_(1-x)Gd_(x)B₁₂ and has ahardness between 38.0 and 52.0 GPa. In some embodiments, a compositematrix is Zr_(1-x)Gd_(x)B₁₂ and has a hardness between 38.0 and 45.0GPa. In some embodiments, a composite matrix is Zr_(1-x)Gd_(x)B₁₂ andhas a hardness between 39.0 and 44.0 GPa. In some embodiments, acomposite matrix is Zr_(1-x)Gd_(x)B₁₂ and has a hardness between 40.0and 44.0 GPa. In some embodiments, a composite matrix isZr_(1-x)Gd_(x)B₁₂ and has a hardness between 41.0 and 43.0 GPa.

In some embodiments, a composite matrix described herein has a grainsize of about 20 μm or less. In some embodiments, the composite matrixhas a grain size of about 15 μm or less, about 12 μm or less, about 10μm or less, about 8 μm or less, about 5 μm or less, about 2 μm or lessor about 1 μm or less. In some embodiments, the composite matrix has agrain size of about 15 μm or less. In some embodiments, the compositematrix has a grain size of about 12 μm or less. In some embodiments, thecomposite matrix has a grain size of about 10 μm or less. In someembodiments, the composite matrix has a grain size of about 9 μm orless. In some embodiments, the composite matrix has a grain size ofabout 8 μm or less. In some embodiments, the composite matrix has agrain size of about 7 μm or less. In some embodiments, the compositematrix has a grain size of about 6 μm or less. In some embodiments, thecomposite matrix has a grain size of about 5 μm or less. In someembodiments, the composite matrix has a grain size of about 4 μm orless. In some embodiments, the composite matrix has a grain size ofabout 3 μm or less. In some embodiments, the composite matrix has agrain size of about 2 μm or less. In some embodiments, the compositematrix has a grain size of about 1 μm or less.

In some embodiments, the grain size is an averaged grain size. In someembodiments, a composite matrix described herein has an averaged grainsize of about 20 μm or less. In some embodiments, the composite matrixhas an averaged grain size of about 15 μm or less, about 12 μm or less,about 10 μm or less, about 8 μm or less, about 5 μm or less, about 2 μmor less or about 1 μm or less. In some embodiments, the composite matrixhas an averaged grain size of about 15 μm or less. In some embodiments,the composite matrix has an averaged grain size of about 12 μm or less.In some embodiments, the composite matrix has an averaged grain size ofabout 10 μm or less. In some embodiments, the composite matrix has anaveraged grain size of about 9 μm or less. In some embodiments, thecomposite matrix has an averaged grain size of about 8 μm or less. Insome embodiments, the composite matrix has an averaged grain size ofabout 7 μm or less. In some embodiments, the composite matrix has anaveraged grain size of about 6 μm or less. In some embodiments, thecomposite matrix has an averaged grain size of about 5 μm or less. Insome embodiments, the composite matrix has an averaged grain size ofabout 4 μm or less. In some embodiments, the composite matrix has anaveraged grain size of about 3 μm or less. In some embodiments, thecomposite matrix has an averaged grain size of about 2 μm or less. Insome embodiments, the composite matrix has an averaged grain size ofabout 1 μm or less.

In some embodiments, a composite matrix described herein is a densifiedcomposite matrix. In some embodiments, a composite matrix describedherein has a density of 10.0 g/cm³ or less. In some embodiments, acomposite matrix described herein has a density of 9.0 g/cm³ or less. Insome embodiments, a composite matrix described herein has a density of8.0 g/cm³ or less. In some embodiments, a composite matrix describedherein has a density of 7.0 g/cm³ or less. In some embodiments, acomposite matrix described herein has a density of 6.0 g/cm³ or less. Insome embodiments, a composite matrix described herein has a density of5.0 g/cm³ or less. In some embodiments, a composite matrix describedherein has a density of 4.0 g/cm³ or less. In some embodiments, acomposite matrix described herein has a density of 3.55 g/cm³ or less.In some embodiments, a composite matrix described herein has a densityof 3.0 g/cm³ or less.

In some embodiments, a composite matrix described herein has a densityof or between 0.1-10.0 g/cm³. In some embodiments, a composite matrixdescribed herein has a density of or between 1.0-9.0 g/cm³. In someembodiments, a composite matrix described herein has a density of orbetween 1.0-8.0 g/cm³. In some embodiments, a composite matrix describedherein has a density of or between 1.0-7.0 g/cm³. In some embodiments, acomposite matrix described herein has a density of or between 2.0-6.0g/cm³. In some embodiments, a composite matrix described herein has adensity of or between 2.0-5.0 g/cm³. In some embodiments, a compositematrix described herein has a density of or between 2.5-4.5 g/cm³. Insome embodiments, a composite matrix described herein has a density ofor between 3.0-4.0 g/cm³.

In some embodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has adensity of 6.0 g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Y_(x)B₁₂ has a density of 5.0 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 4.5g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Y_(x)B₁₂ has a density of 4.0 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of3.75 g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Y_(x)B₁₂ has a density of 3.55 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 3.4g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Y_(x)B₁₂ has a density of 3.0 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Y_(x)B₁₂ has a density of 2.5g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Y_(x)B₁₂ has a density of 2.0 g/cm³ or less.

In some embodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has adensity of 6.0 g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Sc_(x)B₁₂ has a density of 5.0 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of4.0 g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Sc_(x)B₁₂ has a density of 3.5 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of3.35 g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Sc_(x)B₁₂ has a density of 3.1 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of3.0 g/cm³ or less. In some embodiments, a composite matrix ofZr_(1-x)Sc_(x)B₁₂ has a density of 2.5 g/cm³ or less. In someembodiments, a composite matrix of Zr_(1-x)Sc_(x)B₁₂ has a density of2.0 g/cm³ or less.

In some embodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has adensity of 6.0 g/cm³ or less. In some embodiments, a composite matrix ofY_(1-x)Sc_(x)B₁₂ has a density of 5.0 g/cm³ or less. In someembodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 4.0g/cm³ or less. In some embodiments, a composite matrix ofY_(1-x)Sc_(x)B₁₂ has a density of 3.5 g/cm³ or less. In someembodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 3.3g/cm³ or less. In some embodiments, a composite matrix ofY_(1-x)Sc_(x)B₁₂ has a density of 3.21 g/cm³ or less. In someembodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 3.1g/cm³ or less. In some embodiments, a composite matrix ofY_(1-x)Sc_(x)B₁₂ has a density of 3.0 g/cm³ or less. In someembodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of2.75 g/cm³ or less. In some embodiments, a composite matrix ofY_(1-x)Sc_(x)B₁₂ has a density of 2.50 g/cm³ or less. In someembodiments, a composite matrix of Y_(1-x)Sc_(x)B₁₂ has a density of 2.0g/cm³ or less.

In some embodiments, a composite material described herein is resistantto oxidation. In some embodiments, the composite matrix is resistant tooxidation below 550° C. In some embodiments, the composite matrix isresistant to oxidation below 570° C. In some embodiments, the compositematrix is resistant to oxidation below 590° C. In some embodiments, thecomposite matrix is resistant to oxidation below 600° C. In someembodiments, the composite matrix is resistant to oxidation below 610°C. In some embodiments, the composite matrix is resistant to oxidationbelow 620° C. In some embodiments, the composite matrix is resistant tooxidation below 630° C. In some embodiments, the composite matrix isresistant to oxidation below 640° C. In some embodiments, the compositematrix is resistant to oxidation below 650° C. In some embodiments, thecomposite matrix is resistant to oxidation below 660° C. In someembodiments, the composite matrix is resistant to oxidation below 665°C. In some embodiments, the composite matrix is resistant to oxidationbelow 670° C. In some embodiments, the composite matrix is resistant tooxidation below 675° C. In some embodiments, the composite matrix isresistant to oxidation below 680° C. In some embodiments, the compositematrix is resistant to oxidation below 685° C. In some embodiments, thecomposite matrix is resistant to oxidation below 690° C. In someembodiments, the composite matrix is resistant to oxidation below 695°C. In some embodiments, the composite matrix is resistant to oxidationbelow 700° C. In some embodiments, the composite matrix is resistant tooxidation below 725° C. In some embodiments, the composite matrix isresistant to oxidation below 750° C. In some embodiments, the compositematrix is resistant to oxidation below 775° C. In some embodiments, thecomposite matrix is resistant to oxidation below 800° C. In someembodiments, the composite matrix is resistant to oxidation below 825°C. In some embodiments, the composite matrix is resistant to oxidationbelow 850° C. In some embodiments, the composite matrix is resistant tooxidation below 875° C. In some embodiments, the composite matrix isresistant to oxidation below 900° C.

In some embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ andresistant to oxidation below 600° C. In some embodiments, the compositematrix is Zr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 610° C. Insome embodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistantto oxidation below 620° C. In some embodiments, the composite matrix isZr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 630° C. In someembodiments, the composite matrix is Zr_(1-x)Y_(x)B₁₂ and resistant tooxidation below 640° C. In some embodiments, the composite matrix isZr_(1-x)Y_(x)B₁₂ and resistant to oxidation below 650° C.

In some embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ andresistant to oxidation below 600° C. In some embodiments, the compositematrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 620° C. Insome embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ andresistant to oxidation below 640° C. In some embodiments, the compositematrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 660° C. Insome embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ andresistant to oxidation below 670° C. In some embodiments, the compositematrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 675° C. Insome embodiments, the composite matrix is Zr_(1-x)Sc_(x)B₁₂ andresistant to oxidation below 680° C. In some embodiments, the compositematrix is Zr_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 700° C.

In some embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ andresistant to oxidation below 600° C. In some embodiments, the compositematrix is Y_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 620° C. Insome embodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistantto oxidation below 640° C. In some embodiments, the composite matrix isY_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 660° C. In someembodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant tooxidation below 670° C. In some embodiments, the composite matrix isY_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 675° C. In someembodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant tooxidation below 680° C. In some embodiments, the composite matrix isY_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 685° C. In someembodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant tooxidation below 690° C. In some embodiments, the composite matrix isY_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 695° C. In someembodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant tooxidation below 700° C. In some embodiments, the composite matrix isY_(1-x)Sc_(x)B₁₂ and resistant to oxidation below 710° C. In someembodiments, the composite matrix is Y_(1-x)Sc_(x)B₁₂ and resistant tooxidation below 720° C.

In some embodiments, a composite material described herein is resistantto oxidation. In some embodiments, a composite material described hereinhas anti-oxidation property. For example, when the composite material iscoated on the surface of a tool, the composite material reduces the rateof oxidation of the tool in comparison to a tool not coated with thecomposite material. In an alternative example, when the compositematerial is coated on the surface of a tool, the composite materialprevents oxidation of the tool in comparison to a tool not coated withthe composite material. In some embodiments, the composite materialinhibits the formation of oxidation or reduces the rate of oxidation.

In some embodiments, a composite matrix described herein is cubic ortetragonal as determined and characterized by X-ray diffraction. In someembodiments, a composite matrix described herein is cubic. In someembodiments, a composite matrix described herein is cubic and the lengthof a is between 7.350 and 7.550 Å, where a is the length between twoadjacent vertices in the unit cell.

In some embodiments, a composite matrix described herein is tetragonal.In some embodiments, a composite matrix is tetragonal and the length ofa is between 5.150 and 5.450 Å, where a is the shortest length betweentwo adjacent vertices in the unit cell, and the length of c is between7.350 and 7.550 Å, where c is the longest length between two adjacentvertices in the unit cell.

In some embodiments, a composite matrix Zr_(1-x)Y_(x)B₁₂ is cubic andthe length of a is between 7.350 and 7.550 Å, where a is the lengthbetween two adjacent vertices in the unit cell. In some embodiments, acomposite matrix Zr_(1-x)Gd_(x)B₁₂ is cubic and the length of a isbetween 7.350 and 7.550 Å, where a is the length between two adjacentvertices in the unit cell. In some embodiments, a composite matrixZr_(1-x)Sm_(x)B₁₂ is cubic and the length of a is between 7.350 and7.550 Å, where a is the length between two adjacent vertices in the unitcell. In some embodiments, a composite matrix Zr_(1-x)Nd_(x)B₁₂ is cubicand the length of a is between 7.350 and 7.550 Å, where a is the lengthbetween two adjacent vertices in the unit cell. In some embodiments, acomposite matrix Zr_(1-x)Pr_(x)B₁₂ is cubic and the length of a isbetween 7.350 and 7.550 Å, where a is the length between two adjacentvertices in the unit cell. In some embodiments, a composite matrixZr_(1-x)Sc_(x)B₁₂ is tetragonal and the length of a is between 5.150 and5.450 Å, where a is the shortest length between two adjacent vertices inthe unit cell, and the length of c is between 7.350 and 7.550 Å, where cis the longest length between two adjacent vertices in the unit cell. Insome embodiments, a composite matrix Y_(1-x)Sc_(x)B₁₂ is tetragonal andthe length of a is between 5.150 and 5.450 Å, where a is the shortestlength between two adjacent vertices in the unit cell, and the length ofc is between 7.350 and 7.550 Å, where c is the longest length betweentwo adjacent vertices in the unit cell.

In some embodiments, a composite matrix described herein comprises asolid solution phase. In some embodiments, a composite materialdescribed herein forms a solid solution.

Methods of Manufacture

Certain embodiments described herein include methods of making acomposite matrix. Some embodiments described herein comprise a method ofpreparing an oxidative resistant composite matrix, which comprises (a)blending together the boron and metals for a time sufficient to producea powder mixture; (b) pressing the powder mixture under a pressuresufficient to generate a pellet; and (c) sintering the pellet at atemperature sufficient to produce a densified composite matrix.

In some embodiments, the blending time is about 5 minutes to about 6hours. In some embodiments, the blending time is about 5 minutes, about10 minutes, about 15 minutes, about 20 minutes, about 30 minutes, about45 minutes, about 1 hour, about 1.5 hour, about 2 hours, about 3 hours,about 4 hours, about 5 hours, or about 6 hours.

In some embodiments, the blending time is at least 5 minutes or more. Insome embodiments, the blending time is about 10 minutes or more. In someembodiments, the blending time is about 20 minutes or more. In someembodiments, the blending time is about 30 minutes or more. In someembodiments, the blending time is about 45 minutes or more. In someembodiments, the blending time is about 1 hour or more. In someembodiments, the blending time is about 2 hours or more. In someembodiments, the blending time is about 3 hours or more. In someembodiments, the blending time is about 4 hours or more. In someembodiments, the blending time is about 5 hours or more. In someembodiments, the blending time is about 6 hours or more. In someembodiments, the blending time is about 8 hours or more. In someembodiments, the blending time is about 10 hours or more. In someembodiments, the blending time is about 12 hours or more.

In some embodiments, a pressure of up to 36,000 psi is utilized togenerate a pellet. In some embodiments, the pressure is up to 34,000psi. In some embodiments, the pressure is up to 32,000 psi. In someembodiments, the pressure is up to 30,000 psi. In some embodiments, thepressure is up to 28,000 psi. In some embodiments, the pressure is up to26,000 psi. In some embodiments, the pressure is up to 24,000 psi. Insome embodiments, the pressure is up to 22,000 psi. In some embodiments,the pressure is up to 20,000 psi. In some embodiments, the pressure isup to 18,000 psi. In some embodiments, the pressure is up to 16,000 psi.In some embodiments, the pressure is up to 15,000 psi. In someembodiments, the pressure is up to 14,000 psi. In some embodiments, thepressure is up to 10,000 psi.

In some embodiments, the pellets are compressed using a hydraulic press.In some embodiments, the powder is compressed under a 1-20 ton load. Insome embodiments, the powder is compressed under a 2-18 ton load. Insome embodiments, the powder is compressed under a 4-16 ton load. Insome embodiments, the powder is compressed under a 6-14 ton load. Insome embodiments, the powder is compressed under a 8-12 ton load. Insome embodiments, the powder is compressed under a 9-11 ton load.

In some embodiments, the pellets are compressed using a hydraulic press.In some embodiments, the powder is compressed under a 1 ton load. Insome embodiments, the powder is compressed under a 2 ton load. In someembodiments, the powder is compressed under a 3 ton load. In someembodiments, the powder is compressed under a 4 ton load. In someembodiments, the powder is compressed under a 5 ton load. In someembodiments, the powder is compressed under a 6 ton load. In someembodiments, the powder is compressed under a 7 ton load. In someembodiments, the powder is compressed under an 8 ton load. In someembodiments, the powder is compressed under a 9 ton load. In someembodiments, the powder is compressed under a 10 ton load. In someembodiments, the powder is compressed under a 11 ton load. In someembodiments, the powder is compressed under a 12 ton load. In someembodiments, the powder is compressed under a 13 ton load. In someembodiments, the powder is compressed under a 14 ton load. In someembodiments, the powder is compressed under a 15 ton load. In someembodiments, the powder is compressed under a 20 ton load.

In some embodiments, the metal and boron are compressed into a form thatis not a pellet.

In some embodiments, a method described herein further comprises asintering step. In some embodiments, the sintering step generates adensified composite matrix. In some embodiments, the sintering step iscarried out at elevated temperatures. In some embodiments, thetemperature during sintering is from 1000° C. to 2000° C. In someembodiments, the temperature during sintering is from 1000° C. to 1900°C. In some embodiments, the temperature during sintering is from 1200°C. to 1900° C. In some embodiments, the temperature during sintering isfrom 1300° C. to 1900° C. In some embodiments, the temperature duringsintering is from 1400° C. to 1900° C. In some embodiments, thetemperature during sintering is from 1000° C. to 1800° C. In someembodiments, the temperature during sintering is from 1000° C. to 1700°C. In some embodiments, the temperature during sintering is from 1200°C. to 1800° C. In some embodiments, the temperature during sintering isfrom 1300° C. to 1700° C. In some embodiments, the temperature duringsintering is from 1000° C. to 1600° C. In some embodiments, thetemperature during sintering is from 1500° C. to 1800° C. In someembodiments, the temperature during sintering is from 1500° C. to 1700°C. In some embodiments, the temperature during sintering is from 1500°C. to 1600° C. In some embodiments, the temperature during sintering isfrom 1600° C. to 2000° C. In some embodiments, the temperature duringsintering is from 1600° C. to 1900° C. In some embodiments, thetemperature during sintering is from 1600° C. to 1800° C. In someembodiments, the temperature during sintering is from 1600° C. to 1700°C. In some embodiments, the temperature during sintering is from 1700°C. to 2000° C. In some embodiments, the temperature during sintering isfrom 1700° C. to 1900° C. In some embodiments, the temperature duringsintering is from 1700° C. to 1800° C. In some embodiments, thetemperature during sintering is from 1800° C. to 2000° C. In someembodiments, the temperature during sintering is from 1800° C. to 1900°C. In some embodiments, the temperature during sintering is from 1900°C. to 2000° C.

In some embodiments, the temperature is about 1000° C., about 1100° C.,about 1200° C., about 1300° C., about 1400° C., about 1500° C., about1600° C., about 1700° C., about 1800° C., about 1900° C. or about 2000°C. In some embodiments, the temperature is about 1000° C. In someembodiments, the temperature is about 1100° C. In some embodiments, thetemperature is about 1200° C. In some embodiments, the temperature isabout 1300° C. In some embodiments, the temperature is about 1400° C. Insome embodiments, the temperature is about 1500° C. In some embodiments,the temperature is about 1600° C. In some embodiments, the temperatureis about 1700° C. In some embodiments, the temperature is about 1800° C.In some embodiments, the temperature is about 1900° C. In someembodiments, the temperature is about 2000° C.

In some embodiments, sintering is carried out using by electricalcurrent. In some embodiments, sintering is carried out by arc-melting.In some embodiments, arc melting is carried out with a current (I) of 50Amps (A) or more. In some embodiments, arc melting is carried out with aI of 60 A or more. In some embodiments, arc melting is carried out witha I of 65 A or more. In some embodiments, arc melting is carried outwith a I of 70 A or more. In some embodiments, arc melting is carriedout with a I of 75 A or more. In some embodiments, arc melting iscarried out with a I of 80 A or more. In some embodiments, arc meltingis carried out with a I of 90 A or more. In some embodiments, arcmelting is carried out with a I of 100 A or more.

In some embodiments, arc melting is performed in and argon atmosphere.In some embodiments, arc melting is performed in an ultrapure argonatmosphere.

In some embodiments, arc melting is performed for 0.01-10 mins. In someembodiments, arc melting is performed for 0.01-8 mins. In someembodiments, arc melting is performed for 0.01-6 mins. In someembodiments, arc melting is performed for 0.01-5 mins. In someembodiments, arc melting is performed for 0.01-4 mins. In someembodiments, arc melting is performed for 0.5-3 mins. In someembodiments, arc melting is performed for 0.8-2.5 mins. In someembodiments, arc melting is performed for 1-2 mins.

In some embodiments, sintering is carried out at room temperature.

In some embodiment, a sintering step described herein involves anelevated temperature and an elevated pressure, e.g., hot pressing. Hotpressing is a process involving a simultaneous application of pressureand high temperature, which can accelerate the rate of densification ofa material (e.g., a composite matrix described herein). In someembodiments, a temperature from 1000° C. to 2000° C. and a pressure ofup to 36,000 psi are used during hot pressing.

In other embodiments, a sintering step described herein involves anelevated pressure and room temperature, e.g., cold pressing. In suchembodiments, pressure of up to 36,000 psi is used.

Tools and Abrasive Materials

In some embodiments, a composite matrix described herein is used tomake, modify, or coat a tool or an abrasive material. In someembodiments, a composite matrix described herein is coated onto thesurface of a tool or an abrasive material. In some embodiments, thesurface of a tool or an abrasive material is modified with a compositematrix described herein. In some embodiments, the surface of a tool orabrasive material comprises a composite matrix described herein.

In some embodiments, a tool or abrasive material comprises a cuttingtool. In some embodiments, a tool or abrasive material comprises a toolor a component of a tool for cutting, drilling, etching, engraving,grinding, carving, or polishing. In some embodiments, a tool or abrasivematerial comprises a metal bond abrasive tool, for example, such as ametal bond abrasive wheel or grinding wheel. In some embodiments, a toolor abrasive material comprises drilling tools. In some embodiments, atool or abrasive material comprises drill bits, inserts or dies. In someembodiments, a tool or abrasive material comprises tools or componentsused in downhole tooling. In some embodiments, a tool or abrasivematerial comprises an etching tool. In some embodiments, a tool orabrasive material comprises an engraving tool. In some embodiments, atool or abrasive material comprises a grinding tool. In someembodiments, a tool or abrasive material comprises a carving tool. Insome embodiments, a tool or abrasive material comprises a polishingtool.

Certain Terminologies

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as is commonly understood by one of skill in theart to which the claimed subject matter belongs. It is to be understoodthat the detailed description are exemplary and explanatory only and arenot restrictive of any subject matter claimed. In this application, theuse of the singular includes the plural unless specifically statedotherwise. It must be noted that, as used in the specification, thesingular forms “a,” “an” and “the” include plural referents unless thecontext clearly dictates otherwise. In this application, the use of “or”means “and/or” unless stated otherwise. Furthermore, use of the term“including” as well as other forms, such as “include”, “includes,” and“included,” is not limiting.

Although various features of the disclosure may be described in thecontext of a single embodiment, the features may also be providedseparately or in any suitable combination. Conversely, although thedisclosure may be described herein in the context of separateembodiments for clarity, the disclosure may also be implemented in asingle embodiment.

Reference in the specification to “some embodiments”, “an embodiment”,“one embodiment” “another embodiment” or “other embodiments” means thata particular feature, structure, or characteristic described inconnection with the embodiments is included in at least someembodiments, but not necessarily all embodiments, of the disclosure.

As used herein, ranges and amounts can be expressed as “about” aparticular value or range. About also includes the exact amount. Hence“about 5 GPa” means “about 5 GPa” and also “5 GPa.” Generally, the term“about” includes an amount that would be expected to be withinexperimental error, e.g., ±5%, ±10% or ±15%. In some embodiments,“about” includes ±5%. In some embodiments, “about” includes ±10%. Insome embodiments, “about” includes ±15%.

The section headings used herein are for organizational purposes onlyand are not to be construed as limiting the subject matter described.

EXAMPLES

These examples are provided for illustrative purposes only and not tolimit the scope of the claims provided herein.

Example 1. X-Ray Diffraction

Prepared ingots were bisected using a diamond saw (Ameritool Inc.,U.S.A.). One half was crushed into a sub 325 (45 μm) mesh powder andused for powder X-ray diffraction (PXRD) analysis; the other half wasused for energy-dispersive X-ray spectroscopy (EDS) analysis andVicker's hardness measurements. For the latter two, the samples wereencapsulated in epoxy using an epoxy/hardener set (Allied High TechProducts Inc., U.S.A.). In order to achieve an optically flat surface,the samples were polished on a semi-automated polisher (South BayTechnology Inc., U.S.A.), using the following abrasives: SiC discs of120-1200 grit sizes (Allied High Tech Products Inc., U.S.A.) and 30-1micron particle diamond films (South Bay Technology Inc., U.S.A.).

Powder XRD was carried out on a Bruker D8 Discover Powder X-rayDiffractometer (Bruker Corporation, Germany) utilizing Cu_(Kα) X-rayradiation (λ=1.5418 Å). The following scan parameters were used: 5-100°2θ range, time per step of 0.3 sec, step size of 0.0353° with a scanspeed of 0.1055°/sec. In order to determine the phases present in thepowder X-ray diffraction data, the Joint Committee on Powder DiffractionStandards (JCPDS) database was utilized. The composition and purity ofthe samples were determined on an FEI Nova 230 high resolution scanningelectron microscope (FEI Company, U.S.A.) with an UltraDry EDS detector(Thermo Scientific, U.S.A.). Rietveld refinement utilizing Maud softwarewas carried out to determine the cell parameters.

ZrB₁₂, YB₁₂ and ScB₁₂ are completely soluble in each other.Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ undergo a solid-state phasetransition between a cubic and tetragonal cells at 90-95 at % Sc.

Table 1 shows unit cell data for Zr_(1-x)Y_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Y_(x)B₁₂ are shown in FIG. 1.

TABLE 1 Concentration of Y in ZrB₁₂ Cubic (Fm3m) Compound (at. % Y)^(a)a (Å)^(b) a (Å)^(c) ZrB₁₂ — 7.412(2) 7.412 Zr_(0.95)Y_(0.05)B₁₂  2.91(0.10) 7.418(3) 7.417 Zr_(0.75)Y_(0.25)B₁₂ 20.29 (0.12) 7.438(4) 7.435Zr_(0.50)Y_(0.50)B₁₂ 47.81 (0.55) 7.454(3) 7.459 Zr_(0.25)Y_(0.75)B₁₂70.89 (0.46) 7.481(6) 7.482 Zr_(0.05)Y_(0.95)B₁₂ 91.24 (0.41) 7.502(3)7.500 YB₁₂ — 7.505(4) 7.505 ^(a)calculated from EDS analysis; errors aregiven in brackets ^(b)from cell refinement using Maud; errors are givenin brackets ^(c)calculated using Vegard's Law

Table 2 shows unit cell data for Zr_(1-x)Sc_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Sc_(x)B₁₂ are shown in FIG. 2.

TABLE 2 Concentration of Sc in ZrB₁₂ Cubic (Fm3m) Tetragonal (I4/mmm)Compound (at. % Sc)^(a) a (Å)^(b) a (Å)^(b) c (Å)^(b) ZrB₁₂ — 7.412(2) —— Zr_(0.95)Sc_(0.05)B₁₂  2.20 (0.09) 7.412(4) 5.241(2) 7.411(3)Zr_(0.75)Sc_(0.25)B₁₂ 15.14 (0.16) 7.410(3) 5.240(3) 7.410(4)Zr_(0.50)Sc_(0.50)B₁₂ 38.66 (0.28) 7.408(3) 5.237(4) 7.408(5)Zr_(0.25)Sc_(0.75)B₁₂ 65.16 (0.39) 7.405(4) 5.235(2) 7.405(4)Zr_(0.20)Sc_(0.80)B₁₂ 67.49 (0.26) 7.403(2) 5.234(5) 7.402(3)Zr_(0.15)Sc_(0.85)B₁₂ 87.17 (0.33) 7.402(5) 5.233(3) 7.393(3)Zr_(0.10)Sc_(0.90)B₁₂ 90.51 (0.69) 7.398(3) 5.233(4) 7.389(4)Zr_(0.05)Sc_(0.95)B₁₂ 94.97 (0.44) 7.395(3) 5.232(3) 7.385(3) ScB₁₂ — —5.232(3) 7.361(4) ^(a)calculated from EDS analysis; errors are given inbrackets ^(b)from cell refinement using Maud; errors are given inbrackets

Table 3 shows unit cell data for Y_(1-x)Sc_(x)B₁₂. X-ray powderdiffractograms of Y_(1-x)Sc_(x)B₁₂ are shown in FIG. 3.

TABLE 3 Concentration Tetragonal of Sc in YB₁₂ Cubic (Fm3m) (I4/mmm)Compound (at. % Sc)^(a) a (Å)^(b) a (Å)^(b) c (Å)^(b) YB₁₂ — 7.505(4) —— Y_(0.95)Sc_(0.05)B₁₂  4.36 (0.17) 7.504(3) 5.306(2) 7.503(3)Y_(0.75)Sc_(0.25)B₁₂ 26.45 (0.22) 7.486(2) 5.292(3) 7.486(2)Y_(0.50)Sc_(0.50)B₁₂ 40.57 (0.28) 7.486(2) 5.291(4) 7.486(3)Y_(0.25)Sc_(0.75)B₁₂ 65.79 (0.23) 7.455(3) 5.272(2) 7.452(4)Y_(0.20)Sc_(0.80)B₁₂ 67.40 (0.31) 7.448(4) 5.255(5) 7.449(5)Y_(0.15)Sc_(0.85)B₁₂ 73.90 (0.30) 7.442(5) 5.247(5) 7.439(5)Y_(0.10)Sc_(0.90)B₁₂ 81.03 (0.39) 7.428(6) 5.243(3) 7.426(6)Y_(0.05)Sc_(0.95)B₁₂ 92.38 (0.30) 7.402(5) 5.235(2) 7.389(3) ScB₁₂ — —5.232(3) 7.361(4) ^(a)calculated from EDS analysis; errors are given inbrackets ^(b)from cell refinement using Maud; errors are given inbrackets

Table 4 shows unit cell data for Zr_(1-x)Gd_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Gd_(x)B₁₂ are shown in FIG. 4.

TABLE 4 Concentration of Gd in ZB₁₂ Cubic (at % Gd) by (Fm3m) CompoundEDS α, Å Vegard's Law ZrB₁₂ — 7.412(2) 7.412 Zr_(0.95)Gd_(0.05)B₁₂  3.38(0.23) 7.420(3) 7.418 Zr_(0.75)Gd_(0.25)B₁₂ 18.56 (0.31) 7.444(3) 7.440Zr_(0.50)Gd_(0.50)B₁₂ 50.83 (0.80) 7.464(2) 7.468 Zr_(0.45)Gd_(0.55)B₁₂53.70 (0.64) 7.468(2) 7.474 Zr_(0.35)Gd_(0.65)B₁₂ — 7.453(2) 7.485Zr_(0.25)Gd_(0.75)B₁₂ — — 7.496 Zr_(0.05)Gd_(0.95)B₁₂ — — 7.518 GdB₁₂ —7.524 7.524

Table 5 shows unit cell data for Zr_(1-x)Sm_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Sm_(x)B₁₂ are shown in FIG. 5.

TABLE 5 Concentration of Sm in ZB₁₂ Cubic (at % Sm) by (Fm3m) CompoundEDS α, Å ZrB₁₂ — 7.412(2) Zr_(0.95)Sm_(0.05)B₁₂  2.93 (0.42) 7.419(3)Zr_(0.75)Sm_(0.25)B₁₂ 14.94 (0.24) 7.433(3) Zr_(0.70)Sm_(0.30)B₁₂ 13.99(0.23) 7.431(4) Zr_(0.65)Sm_(0.35)B₁₂ — 7.429(2) Zr_(0.50)Sm_(0.50)B₁₂ —7.428(3) SmB₁₂ — 7.543

Table 6 shows unit cell data for Zr_(1-x)Nd_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Nd_(x)B₁₂ are shown in FIG. 6.

TABLE 6 Concentration of Nd in ZB₁₂ Cubic (at % Nd) by (Fm3m) CompoundEDS a, Å ZrB₁₂ — 7.412(2) Zr_(0.95)Nd_(0.05)B₁₂ 1.76 (0.11) 7.413(3)Zr_(0.75)Nd_(0.25)B₁₂ 7.17 (0.28) 7.421(2) Zr_(0.50)Nd_(0.50)B₁₂ —7.419(3)

Table 7 shows unit cell data for Zr_(1-x)Pr_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Pr_(x)B₁₂ are shown in FIG. 7.

TABLE 7 Concentration of Pr in ZB₁₂ Cubic (at % Pr) by (Fm3m) CompoundEDS a, Å ZrB₁₂ — 7.412(2) Zr_(0.95)Pr_(0.05)B₁₂ 1.61 (0.22) 7.415(2)Zr_(0.75)Pr_(0.25)B₁₂ 4.12 (0.27) 7.418(4) Zr_(0.50)Pr_(0.50)B₁₂ —7.418(3)

The solubility limit of Gd in ZrB₁₂ is 54 at. % Gd. The solubility limitof Sm in ZrB₁₂ is ˜15 at. % Sm. The solubility limit of Pr in ZrB₁₂ is 4at. % Pr. The solubility limit of Nd in ZrB₁₂ is ˜7 at. % Nd. Withincreasing concentration of Gd, Sm, Nd and Pr, the dodecaboride (MB₁₂)phase concentration decreases while the hexaboride (MB₆) phaseincreases. In most cases, the higher boride phases ZrB₅₀, GdB₆₆, SmB₆₆or NdB₆₆ can be observed in the XRPD diffractograms as they accompanythe dodecaboride phases at higher metal to boron ratios (1:20).

Table 8 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Zr_(1-x)Y_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Y_(x)B₁₂ are shown in FIG. 1.

TABLE 8 Zr_(0.95)Y_(0.05)B₁₂ Zr_(0.75)Y_(0.25)B₁₂ Zr_(0.50)Y_(0.50)B₁₂ #h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.702665.05 20.6860 37.89 20.6081 69.57 2 2 0 0 23.9694 64.27 23.9341 54.4023.8622 77.51 3 2 2 0 34.1433 21.65 34.0958 24.04 34.0068 27.27 4 3 1 140.2907 100.00 40.2119 100.00 40.0759 100.00 5 2 2 2 42.1499 26.4042.0686 19.27 41.9283 23.75 6 4 0 0 49.0685 7.41 48.9665 6.47 48.80238.91 7 3 3 1 53.8300 24.41 53.6957 22.82 53.5130 16.60 8 4 2 0 55.335713.16 55.2003 7.92 55.0155 12.68 9 4 2 2 61.1600 24.42 61.0321 17.5460.7954 22.83 10 5 1 1 65.3232 7.13 65.1830 6.34 64.9327 7.28 11 4 4 072.0237 1.56 71.8198 1.38 71.6078 2.42 12 5 3 1 75.8257 24.75 75.627118.14 75.5588 19.34 13 4 4 2 76.0645 13.42 76.9139 10.46 75.5950 13.9714 6 2 0 77.0849 12.89 77.0707 7.95 76.8519 10.56 15 5 3 3 82.1129 4.8881.8678 3.52 81.7783 5.01 16 6 2 2 85.8314 3.67 85.5586 2.30 86.63181.18 Zr_(0.25)Y_(0.75)B₁₂ Zr_(0.05)Y_(0.95)B₁₂ # h k l 2Θ° I_(rel) (%)2Θ° I_(rel) (%)  1 1 1 1 20.5293 89.17 20.5005 54.05  2 2 0 0 23.754378.40 23.6942 57.73  3 2 2 0 33.8576 35.08 33.7629 24.24  4 3 1 139.9183 100.00 39.8357 100.00  5 2 2 2 41.7846 32.82 41.6885 26.07  6 40 0 48.6299 8.44 48.5042 7.22  7 3 3 1 53.3210 28.35 53.1733 22.49  8 42 0 54.8221 17.32 54.6886 12.24  9 4 2 2 60.5763 26.41 60.4185 19.78 105 1 1 64.6989 15.25 64.4951 6.53 11 4 4 0 71.2255 3.49 71.0455 2.07 12 53 1 75.0477 20.23 74.8398 17.22 13 4 4 2 76.3177 18.68 76.0826 11.69 146 2 0 81.2397 6.12 81.0299 4.42 15 5 3 3 84.9269 5.11 84.6614 5.16 16 62 2 86.1455 2.02 85.8526 2.00

Table 9 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Zr_(1-x)Sc_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Sc_(x)B₁₂ are shown in FIG. 2.

TABLE 9 Zr_(0.95)Sc_(0.05)B₁₂ Zr_(0.75)Sc_(0.25)B₁₂Zr_(0.50)Sc_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ°I_(rel) (%) 1 1 1 1 20.7178 58.46 20.7398 85.98 20.7361 57.70 2 2 0 023.9943 93.95 23.9757 85.23 23.9854 69.11 3 2 2 0 34.1912 31.37 34.190825.12 34.2016 24.02 4 3 1 1 40.3082 100.00 40.3168 100.00 40.3385 100.005 2 2 2 42.1836 22.92 42.1884 36.65 42.2354 26.93 6 4 0 0 49.1145 11.9549.1069 9.17 49.1542 6.04 7 3 3 1 53.8591 23.18 53.8572 25.82 53.874514.22 8 4 2 0 55.3704 14.53 55.3652 13.17 55.3818 6.77 9 4 2 2 61.190027.28 61.1908 20.34 61.2867 15.71 10 5 1 1 65.4171 7.55 65.3704 6.5765.4610 4.79 11 4 4 0 72.1084 2.43 72.1090 1.86 72.0250 0.89 12 5 3 175.8802 19.46 75.8806 26.93 75.8868 12.03 13 4 4 2 77.1615 18.47 77.145614.45 77.1449 7.27 14 6 2 0 77.3937 10.51 77.3910 7.38 82.0000 0.89 15 53 3 82.2883 3.16 82.1628 4.53 85.9550 1.06 16 6 2 2 85.9958 2.58 85.88913.36 87.4250 0.45 Zr_(0.25)Sc_(0.75)B₁₂ Zr_(0.20)Sc_(0.80)B₁₂Zr_(0.15)Sc_(0.85)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ°I_(rel) (%) 1 1 1 1 20.7626 44.77 20.7630 43.33 20.7648 48.83 2 2 0 024.0221 49.49 24.0289 68.73 24.0413 70.87 3 2 2 0 34.2209 16.61 34.229318.19 34.2271 16.89 4 3 1 1 40.3772 100.00 40.3784 100.00 40.3824 100.005 2 2 2 42.2572 25.52 42.2533 29.31 42.2827 37.10 6 4 0 0 49.3728 3.6649.5156 3.62 49.4817 6.04 7 3 3 1 53.9280 18.53 53.9717 16.72 53.971920.02 8 4 2 0 55.4717 7.39 55.5050 31.28 55.5050 23.59 9 4 2 2 61.252714.18 61.3084 16.90 61.3268 20.89 10 5 1 1 65.1090 3.08 65.1321 2.8465.0131 4.84 11 4 4 0 72.2350 1.38 72.0628 6.45 72.2350 18.08 12 5 3 175.9964 13.67 75.9738 12.33 75.9878 13.78 13 4 4 2 77.2635 9.98 77.35725.72 77.2838 10.53 14 6 2 0 82.5950 0.75 15 5 3 3 85.9833 2.19 16 6 2 2

Table 10 shows the hkl, 2Theta and intensity values for a tetragonaldodecaboride alloy of the formula X-ray powder diffractograms ofZr_(1-x)Sc_(x)B₁₂ are shown in FIG. 2.

TABLE 10 Zr_(0.10)Sc_(0.90)B₁₂ Zr_(0.05)Sc_(0.95)B₁₂ No. h k l 2Θ°I_(rel) (%) 2Θ° I_(rel) (%) 1 1 0 1 20.7899 29.49 20.7772 31.36 2 1 1 023.8350 44.55 23.8350 49.04 3 0 0 2 24.0564 54.16 24.0513 70.20 4 2 0 034.2377 11.90 33.9100 6.69 5 1 1 2 34.5400 7.24 34.2402 11.58 6 2 1 140.4064 100.00 40.3898 100.00 7 1 0 3 40.7377 10.13 40.7000 28.20 8 2 02 42.2998 23.22 42.2791 35.66 9 2 2 0 49.3360 6.21 49.3193 8.80 10 0 0 449.4133 14.18 49.6600 9.44 11 3 0 1 54.0191 15.30 53.6500 8.57 12 2 1 354.3280 12.89 54.0017 13.96 13 3 1 0 55.0850 10.11 55.2600 0.96 14 2 2 255.2961 8.18 55.5413 10.74 15 1 1 4 55.5050 12.19 56.0454 6.90 16 3 1 261.3601 16.07 61.3731 15.03 17 2 0 4 61.7989 7.05 61.8050 6.29 18 3 2 165.0957 4.68 65.2700 8.15 19 3 0 3 65.5681 12.43 65.7882 6.16

Table 11 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Y_(1-x)Sc_(x)B₁₂. X-ray powderdiffractograms of Y_(1-x)Sc_(x)B₁₂ are shown in FIG. 3.

TABLE 11 Y_(0.95)Sc_(0.05)B₁₂ Y_(0.75)Sc_(0.25)B₁₂ Y_(0.50)Sc_(0.50)B₁₂# h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.496458.91 20.5313 24.38 20.5203 57.33 2 2 0 0 23.6981 69.81 23.7549 28.9223.7511 67.95 3 2 2 0 33.7648 26.79 33.8449 9.91 33.8601 23.15 4 3 1 139.8090 100.00 39.9113 52.32 39.9198 100.00 5 2 2 2 41.6500 31.9641.8200 100.00 41.7777 30.08 6 4 0 0 48.4679 10.35 48.6098 3.31 48.66237.08 7 3 3 1 53.1722 22.19 53.3092 9.14 53.3144 20.98 8 4 2 0 54.663512.91 54.8020 4.65 54.8313 10.35 9 4 2 2 60.3876 22.63 60.5436 9.6960.6240 17.76 10 5 1 1 64.4640 8.20 64.6994 2.10 64.7165 6.65 11 4 4 071.0483 3.13 71.2645 0.94 71.2974 2.12 12 5 3 1 74.7960 20.36 75.01078.10 75.0668 17.48 13 4 4 2 76.0474 14.68 76.2729 6.06 76.3554 10.94 146 2 0 80.9737 4.60 81.3056 1.28 81.2300 5.22 15 5 3 3 84.6176 3.8984.8937 0.74 85.0192 2.50 16 6 2 2 85.8930 1.54 Zr_(0.25)Sc_(0.75)B₁₂Zr_(0.20)Sc_(0.80)B₁₂ Zr_(0.15)Sc_(0.85)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ°I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.6260 36.04 20.6223 43.59 20.669346.39 2 2 0 0 23.8742 59.79 23.8791 73.79 23.8890 76.43 3 2 2 0 34.015813.77 34.0136 16.58 34.0796 13.94 4 3 1 1 40.0964 100.00 40.0985 100.0040.1674 100.00 5 2 2 2 41.9741 21.08 41.9675 30.89 42.0556 31.36 6 4 0 048.8722 6.71 48.8909 7.82 48.9411 7.33 7 3 3 1 53.5244 13.88 53.569817.62 53.6881 12.43 8 4 2 0 55.0798 8.18 55.0734 7.11 55.1616 5.71 9 4 22 60.8667 16.75 60.8407 18.16 60.9368 17.02 10 5 1 1 64.9627 4.0564.8644 4.90 65.0012 3.82 11 4 4 0 71.5700 1.42 71.5206 5.16 71.57001.17 12 5 3 1 75.4180 14.93 75.3873 11.57 75.5552 12.63 13 4 4 2 76.678212.64 76.6810 11.11 76.8241 12.74 14 6 2 0 81.4400 0.69 81.5800 1.52 155 3 3 85.2900 1.02 85.3950 2.11 16 6 2 2

Table 12 shows the hkl, 2Theta and intensity values for a tetragonaldodecaboride alloy of the formula Y_(1-x)Sc_(x)B₁₂. X-ray powderdiffractograms of Y_(1-x)Sc_(x)B₁₂ are shown in FIG. 3.

TABLE 12 Y_(0.10)Sc_(0.90)B₁₂ Y_(0.05)Sc_(0.95)B₁₂ No. h k l 2Θ° I_(rel)(%) 2Θ° I_(rel) (%) 1 1 0 1 20.6812 41.26 20.7148 41.80 2 1 1 0 23.558111.32 23.9050 81.86 3 0 0 2 23.9516 55.72 24.2200 37.24 4 2 0 0 33.77005.68 33.8900 8.78 5 1 1 2 34.1744 11.65 34.1939 20.50 6 2 1 1 40.2395100.00 40.3298 100.00 7 1 0 3 40.5600 21.25 40.6726 17.35 8 2 0 242.1047 32.41 42.2141 42.34 9 2 2 0 49.0650 15.93 49.1700 28.96 10 0 0 449.4813 13.99 49.4740 24.64 11 3 0 1 52.9850 12.70 53.9185 15.60 12 2 13 53.7835 16.46 54.3885 22.43 13 3 1 0 54.7227 6.22 55.3699 13.83 14 2 22 55.2600 11.79 55.7155 10.26 15 1 1 4 55.6966 5.79 55.8742 11.52 16 3 12 61.0459 18.75 61.2640 16.93 17 2 0 4 61.4550 10.68 61.3500 31.17 18 32 1 64.9498 4.16 65.2267 11.14 19 3 0 3 65.3774 8.52 65.5369 14.65

Table 13 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Zr_(1-x)Gd_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Gd_(x)B₁₂ are shown in FIG. 4.

TABLE 13 Zr_(0.95)Gd_(0.05)B₁₂ Zr_(0.75)Gd_(0.25)B₁₂Zr_(0.50)Gd_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ°I_(rel) (%) 1 1 1 1 20.7399 95.93 20.6788 87.10 20.6085 93.87 2 2 0 024.0003 85.05 23.9010 73.41 23.8416 83.62 3 2 2 0 34.1848 29.59 34.078832.10 33.9797 41.84 4 3 1 1 40.3161 100.00 40.1971 100.00 40.0610 100.005 2 2 2 42.1798 35.81 42.0875 31.49 41.9272 43.00 6 4 0 0 49.1039 10.7948.9955 7.29 48.7397 11.55 7 3 3 1 53.8340 20.77 53.6851 26.60 53.504523.29 8 4 2 0 55.3630 11.94 55.2286 13.31 55.0078 13.05 9 4 2 2 61.175922.15 61.0029 23.17 60.7900 34.39 10 5 1 1 65.3611 8.13 65.1884 10.3464.9650 7.17 11 4 4 0 72.0117 2.51 71.7155 9.94 71.4914 13.80 12 5 3 175.8327 14.63 75.5956 16.24 75.3063 28.32 13 4 4 2 76.0695 7.55 76.864913.25 76.5720 23.79 14 6 2 0 77.1034 12.00 77.0441 12.19 81.5100 5.09 155 3 3 82.1064 2.63 81.8641 2.97 85.1850 4.84 16 6 2 2 85.8590 2.3585.6050 1.97 86.5150 2.00 Zr_(0.55)Gd_(0.45)B₁₂ Zr_(0.65)Gd_(0.35)B₁₂ #h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.6071 83.86 20.6387100.00 2 2 0 0 23.8274 100.00 23.8697 65.41 3 2 2 0 33.9574 42.0534.0230 38.09 4 3 1 1 40.0382 95.84 40.1173 97.72 5 2 2 2 41.8981 24.8242.0336 32.66 6 4 0 0 48.8118 9.80 53.6360 19.07 7 3 3 1 53.4668 26.0854.6538 72.77 8 4 2 0 54.9771 18.14 60.8403 22.59 9 4 2 2 60.7139 21.0865.2000 35.84 10  5 1 1 64.8691 10.12 71.6913 36.39 11  4 4 0 71.640014.96 75.4766 15.27 12  5 3 1 75.2413 28.80 76.7779 15.57 13  4 4 276.4965 21.71 14  6 2 0 81.6850 4.64 15  5 3 3 16  6 2 2

Table 14 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Zr_(1-x)Sm_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Sm_(x)B₁₂ are shown in FIG. 5.

TABLE 14 Zr_(0.95)Sm_(0.05)B₁₂ Zr_(0.75)Sm_(0.25)B₁₂Zr_(0.70)Sm_(0.30)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ°I_(rel) (%) 1 1 1 1 20.7436 85.19 20.7049 87.59 20.7140 76.55 2 2 0 023.9854 77.80 23.9708 72.65 23.9607 84.46 3 2 2 0 34.1869 31.82 34.124232.90 34.1286 23.74 4 3 1 1 40.3040 100.00 40.2444 100.00 40.2499 100.005 2 2 2 42.1811 34.25 42.1192 32.38 42.1361 26.58 6 4 0 0 49.1089 9.9749.2909 21.98 49.2748 27.84 7 3 3 1 53.8419 24.99 53.7459 35.20 53.753022.20 8 4 2 0 55.3619 13.12 55.2524 17.75 55.3325 12.38 9 4 2 2 61.193820.73 61.0529 22.71 61.1205 15.11 10 5 1 1 65.3383 8.49 65.2486 8.0465.2905 6.50 11 4 4 0 72.0605 1.86 72.2724 11.71 72.2350 17.32 12 5 3 175.8377 19.15 75.6644 19.66 75.6771 17.62 13 4 4 2 77.1195 11.80 76.935012.94 76.9644 10.02 14 6 2 0 82.1043 2.24 81.7900 0.81 82.2450 1.85 15 53 3 85.9068 1.15 82.1400 1.39 16 6 2 2 87.1150 1.01 85.7309 2.37Zr_(0.50)Sm_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%)  1 1 1 1 20.7265 83.37  22 0 0 23.9744 90.90  3 2 2 0 34.1616 25.18  4 3 1 1 40.2558 92.10  5 2 22 42.1358 45.35  6 4 0 0 49.2995 100.00  7 3 3 1 53.7991 25.05  8 4 2 055.3094 16.46  9 4 2 2 61.1152 30.72 10 5 1 1 71.6165 14.78 11 4 4 075.6890 20.49 12 5 3 1 76.1900 21.82 13 4 4 2 14 6 2 0 15 5 3 3 16 6 2 2

Table 15 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Zr_(1-x)Nd_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Nd_(x)B₁₂ are shown in FIG. 6.

TABLE 15 Zr_(0.95)Nd_(0.05)B₁₂ Zr_(0.75)Nd_(0.25)B₁₂Zr_(0.50)Nd_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ°I_(rel) (%) 1 1 1 1 20.7586 74.00 20.7497 83.40 20.7456 72.77 2 2 0 024.0140 78.92 23.9956 87.59 24.0122 57.89 3 2 2 0 34.1997 29.66 34.197533.63 34.1936 28.35 4 3 1 1 40.3216 100.00 40.3224 100.00 40.3400 87.055 2 2 2 42.2093 29.42 42.1930 37.94 42.2002 27.22 6 4 0 0 49.1216 10.3049.3062 31.64 49.3139 100.00 7 3 3 1 53.8682 28.24 53.8432 23.94 53.895919.68 8 4 2 0 55.3969 10.73 55.3794 12.80 55.4135 26.69 9 4 2 2 61.206320.87 61.1851 25.96 61.2281 14.60 10 5 1 1 65.3797 6.37 65.3465 7.9365.3098 16.94 11 4 4 0 72.0496 3.01 71.7800 0.58 72.1300 22.45 12 5 3 175.8700 17.10 75.8255 19.07 76.0967 7.76 13 4 4 2 77.1479 9.71 77.093312.63 77.4150 2.87 14 6 2 0 82.2448 1.78 82.1980 2.20 15 5 3 3 85.87122.90 84.3800 0.53

Table 16 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Zr_(1-x)Pr_(x)B₁₂. X-ray powderdiffractograms of Zr_(1-x)Pr_(x)B₁₂ are shown in FIG. 7.

TABLE 16 Zr_(0.95)Pr_(0.05)B₁₂ Zr_(0.75)Pr_(0.25)B₁₂Zr_(0.50)Pr_(0.50)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ°I_(rel) (%) 1 1 1 1 20.7375 92.84 20.7495 70.17 20.7476 64.31 2 2 0 024.0010 93.37 24.0094 72.41 24.0090 49.77 3 2 2 0 34.1815 25.89 34.204833.50 34.2222 17.60 4 3 1 1 40.3346 100.00 40.3362 100.00 40.3419 72.075 2 2 2 42.1989 37.76 42.2141 32.24 42.2263 29.16 6 4 0 0 49.1034 11.1249.2052 31.88 49.2283 100.00 7 3 3 1 53.8531 31.81 53.8757 21.71 53.58001.12 8 4 2 0 55.3989 14.05 55.4408 10.53 55.7129 9.53 9 4 2 2 61.202623.30 61.2064 22.90 61.2131 13.05 10 5 1 1 65.3592 8.08 65.4264 4.8165.4100 21.87 11 4 4 0 72.1605 2.68 72.1542 10.53 72.2167 24.70 12 5 3 175.8634 22.19 75.8540 14.84 75.8402 18.39 13 4 4 2 77.1447 16.97 77.10398.19 77.2670 15.13 14 6 2 0 82.4289 1.84 82.0000 0.95 82.3500 1.49 15 53 3 85.8500 2.39

Table 17 shows the hkl, 2Theta and intensity values for a cubicdodecaboride alloy of the formula Zr_(1-x)Y_(x)B₁₂ prepared using ametal to boron ratio of 1 to 13. X-ray powder diffractograms ofZr_(1-x)Y_(x)B₁₂ prepared using a metal to boron ratio of 1 to 13 shownin FIG. 14.

TABLE 17 Zr_(0.95)Y_(0.05)B₁₂ Zr_(0.75)Y_(0.25)B₁₂ Zr_(0.50)Y_(0.50)B₁₂# h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 2Θ° I_(rel) (%) 1 1 1 1 20.735573.46 20.7002 71.95 20.6212 69.98 2 2 0 0 23.9946 60.6 23.9456 65.3323.8571 77.65 3 2 2 0 34.1996 28.06 34.1128 25.85 33.9807 27.32 4 3 1 140.3165 100 40.215 100 40.075 100 5 2 2 2 42.1942 28.85 42.0944 30.9941.9376 32.52 6 4 0 0 49.1008 6.89 48.9676 6.71 48.8143 10.82 7 3 3 153.8424 27.08 53.7116 21.46 53.5215 25.2 8 4 2 0 55.3707 12.53 55.222112.41 55.0229 15.1 9 4 2 2 61.1854 26.71 61.0171 21.66 60.809 23.52 10 51 1 65.3368 8.26 65.1641 6.72 64.9404 9.71 11 4 4 0 72.0002 3.37 71.7723.03 71.5162 2.87 12 5 3 1 75.8539 21.49 75.6176 18.01 75.3481 19.97 134 4 2 76.0955 11.12 75.8566 9.18 76.6094 15.09 14 6 2 0 77.1219 14.776.8815 12.12 81.5983 4.52 15 5 3 3 82.1404 4.03 81.8827 4.27 81.84142.29 16 6 2 2 85.871 2.66 85.6007 2.79 85.5583 1.55 Zr_(0.25)Y_(0.75)B₁₂Zr_(0.05)Y_(0.95)B₁₂ # h k l 2Θ° I_(rel) (%) 2Θ° I_(rel) (%)  1 1 1 120.5795 52.79 20.5188 61.69  2 2 0 0 23.8051 56.88 23.7555 65.07  3 2 20 33.9166 26.82 33.8219 29.93  4 3 1 1 39.9739 100 39.8751 100  5 2 2 241.8384 26.55 41.726 26.86  6 4 0 0 48.6771 6.93 48.5698 7.06  7 3 3 153.3717 19.66 53.2352 22.3  8 4 2 0 54.8634 13.03 54.7391 18.77  9 4 2 260.6127 18.23 60.4644 20.74 10 5 1 1 64.7274 6.11 64.5777 7.42 11 4 4 071.2913 2.97 71.1007 2.69 12 5 3 1 75.0889 16.1 74.8923 16.5 13 4 4 275.3243 8.28 76.1436 10.82 14 6 2 0 76.3386 10.86 76.3831 5.71 15 5 3 381.2894 3.03 81.0903 3.84 16 6 2 2 84.9457 2.19 84.7505 2.73

Example 2. Hardness Determination

The hardness of each sample was determined using a MicroMet 2103 Vickersmicrohardness tester (Buehler Ltd, U.S.A.). Fifteen indents of thefollowing force loading were made in random areas of the sample: 0.49,0.98, 1.96, 2.94 and 4.9 N (low to high, respectively). The length ofthe diagonals were measured using a high resolution optical microscope(Zeiss Axiotech 100HD, Carl Zeiss Vision GmbH, Germany) with 500×magnification, and Vickers hardness was calculated using Equation 1:

$\begin{matrix}{H_{v} = \frac{1854.4F}{a^{2}}} & (1)\end{matrix}$where F is the loading force applied in Newton (N) and a is the averageof the length of the two diagonals of each indent in micrometers.

Measurements of Vickers microindentation hardness of Zr_(1-x)Y_(x)B₁₂are shown in FIG. 8.

Measurements of Vickers microindentation hardness of Zr_(1-x)Sc_(x)B₁₂are shown in FIG. 9.

Measurements of Vickers microindentation hardness of Y_(1-x)Sc_(x)B₁₂are shown in FIG. 10.

Measurements of Vickers microindentation hardness of Zr_(1-x)Gd_(x)B₁₂are shown in FIG. 11.

Example 3. Oxidation Resistance

Oxidation resistance was determined via thermogravimetric analysisutilizing a Pyris Diamond TGA/DTA unit (TG-DTA, Perkin-ElmerInstruments, U.S.A.). The following heating/cooling profile was used:heating in air from 25 to 200° C. (at 20° C./min), holding at 200° C.for 30 minutes, heating from 200 to 1000° C. (at 2° C./min), holding at1000° C. for 120 minutes, cooling 1000 to 25° C. (at 5° C./min).

FIG. 12 shows the thermal stability of pure ZrB₁₂, YB₁₂ and ScB₁₂ andthe hardest solid solutions of mixed metal dodecaborides as measured bythermal gravimetric analysis in air. These data show thatZr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂ arestable up to ˜630° C., ˜685° C. and ˜695° C., respectively (using theextrapolated oxidation onset), compared to ˜610° C. for pure ZrB₁₂,˜715° C. for pure YB₁₂ and ˜685° C. pure ScB₁₂.

FIG. 13 shows the thermal stability of pure ZrB₁₂, Zr_(0.5)Gd_(0.5)B₁₂and Zr_(0.75)Sm_(0.25)B₁₂ as measured by thermal gravimetric analysis inair. These data show that Zr_(0.5)Gd_(0.5)B₁₂ is stable up to ˜630° C.,while Zr_(0.75)Sm_(0.25)B₁₂ up to ˜620° C., compared to ˜610° C. forpure ZrB₁₂.

Example 4. Preparation

Mixed dodecaboride solid solutions, Zr_(1-x)Y_(x)B₁₂, (x=0.00, 0.05,0.25, 0.50, 0.75, 0.95 and 1.00), Zr_(1-y)Sc_(y)B₁₂, Y_(1-y)Sc_(y)B₁₂(y=0.00, 0.05, 0.25, 0.50, 0.75, 0.80, 0.85, 0.90, 0.95 and 1.00), ScB₅₀and YB₆₆ were synthesized using metal and boron powders of high-purity:amorphous boron (99+%, Strem Chemicals, U.S.A.), zirconium (99.5%, StremChemicals, U.S.A.), yttrium (99.9%, Strem Chemicals, U.S.A.) andscandium (99.9%, Sigma-Aldrich, U.S.A.). In order to prevent theformation of the lower boride phases, a metals to boron ratio of 1:20was used for the dodecaborides, 1:65 for ScB₅₀ and 1:70 for YB₆₆. Thepowders of boron and transition metals were weighed, homogenized in anagate mortar and pestle and pressed into pellets using a hydraulic press(Carver) under a 10 ton load. The samples were then arc-melted (I≥70amps, t=1-2 mins) in an ultra-high purity argon atmosphere.

Pellets of Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Pr_(x)B₁₂, andZr_(1-x)Nd_(x)B₁₂ (x=0.05, 0.25, 0.50, 0.75, and 0.95) were preparedusing high-purity metal and boron powders: amorphous boron (99+%, StremChemicals), gadolinium (99%, Sigma-Aldrich), zirconium (99.5%, StremChemicals), samarium (Strem Chemicals, 99.9%), praseodymium (99.9%,Strem Chemicals), and neodymium (99.8%, Strem Chemicals). The metal toboron ratio was kept at a minimum of 1:20 to prevent the formation oflower borides (MB₆) as they are the most stable boride phases of Gd, Sm,Nd, and Pr at ambient pressure. The weighed mixtures were homogenized invials in a vortex mixer for ˜1 min, and then consolidated in a hydraulicpress (Carver) under 10 tons before being arc melted (I>70 A, T=1-2 min)under a high purity argon atmosphere.

Example 5. Unit Cell Analysis

Metal dodecaborides (MB₁₂) constitute a class of boron rich compoundspreviously studied for their magnetic, optical and electronicproperties. The structure of all dodecaborides contains boroncuboctahedron cages composed of 24 atoms, each containing a12-coordinate metal in its center. The cages are usually arranged in aface-centered cubic close packed arrangement, forming the cubic-UB₁₂(Fm3m) structure; however, ScB₁₂ forms its own structuraltype—tetragonal-ScB₁₂ (I4/mmm), where the cuboctahedra are arranged in abody-centered tetragonal close-packed structure.

FIG. 15 shows the unit cell of the cubic-UB₁₂ (top left) dodecaboridestructure type: metal atoms are in blue, B atoms in yellow, (top right)cubic-UB₁₂ polyhedra model: face-centered cubic (FCC) lattice of 24boron atom cuboctahedra boron cages surrounding 12-coordinate metalatoms; (bottom left) the unit cell of the tetragonal-ScB₁₂ dodecaboridestructure type: metal atoms are in magenta, B atoms in yellow, (bottomright) tetragonal-ScB₁₂ polyhedra model: body-centered tetragonal (BCT)lattice of 24 boron atom cuboctahedra boron cages surrounding12-coordinate metal atoms. Note, while 24 borons surround each metalatom, each metal atom is equidistant from 12 B—B bonds, making it12-coordinate.

FIG. 16 shows the crystal structure of ScB₅₀, known as theβ-rhombohedral boron doping phase of scandium (Inorganic CrystalStructure Database (ICSD) 2204, space group R3m), showing characteristicboron icosahedra; (right) crystal structure of YB₆₆ (ICSD 23186, spacegroup Fm3c). (Boron atoms, which are part of B₁₂ clusters are shown asgreen icosahedra, other boron atoms are in dark red, scandium atoms arein violet, yttrium atoms are in teal).

FIG. 17 shows a polyhedra model of the unit cell of a cubic-UB₁₂structural type metal dodecaboride (top left): 24 boron atomcuboctahedra cages (square faces shown in red, hexagonal face in green)are arranged in a FCC lattice, with a 12-coordinate metal atom in thecenter of each cage; (top right) polyhedra model of the unit cell of atetragonal-ScB₁₂ structural type metal dodecaboride: 24 boron atomcuboctahedra cages (square faces shown in red, hexagonal facein green)are arranged in a BCT lattice, with a 12-coordinate metal atom in thecenter of each cage; Note, metals are considered 12-coordinate since 12boron-boron bonds are equidistant from each metal atom in the 24 boronatom cuboctahedron cage; (bottom left) polyhedra model of the unit cellof a rhombohedral-MB₅₀ structural type (solid solution of a metal inβ-rhombohedral boron): boron atoms are arranged in B₁₂ icosahedral units(shown in green), metal atoms are in blue; (bottom right) polyhedramodel of the unit cell of a cubic-YB₆₆ structural type metal boride:boron atoms are arranged in B₁₂ icosahedral units (shown in green),boron atoms not forming icosahedra are in red, metal atoms are in blue.

Example 6. Energy Dispersive X-Ray Analysis (EDS)

Elemental maps and SEM images of selected samples of Zr_(1-x)Gd_(x)B₁₂,Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ alloys(x=0.55, 0.30, 0.25 and 0.25 respectively) are presented in FIG. 18.Elemental maps for boron (K line), zirconium (L line) and gadolinium,samarium, neodymium and praseodymium (L lines) of: (a) theZr_(0.45)Gd_(0.55)B₁₂ solid solution showing the presence of zirconiumand gadolinium in the dodecaboride phase. The boron rich areascorrespond to a higher boride phase GdB₆₆ (cubic, Fm3c structure,a=23.449 Å, ICSD (Inorganic Crystal Structure Database) 614306); (b) theZr_(0.70)Sm_(0.30)B₁₂ solid solution showing the presence of zirconiumand samarium in the dodecaboride phase. The samarium rich areascorrespond to SmB₆ (cubic, Pm3m structure, a=4.133 Å, ICSD 194196),while the boron rich areas correspond to a higher boride phase SmB₆₆(cubic, Fm3c structure, a=23.468 Å). (c) the Zr_(0.75)Nd_(0.25)B₁₂ solidsolution showing the presence of zirconium and neodymium in thedodecaboride phase. The neodymium rich areas correspond to NdB₆ (cubic,Pm3m structure, a=4.127 Å, ICSD 614931), while the boron rich areascorrespond to a higher boride phase NdB₆₆ (cubic, Fm3c structure,a=23.476 Å) and ZrB₅₀ (rhombohedral, R3m structure, a=10.932 Å, c=23.849Å); (d) the Zr_(0.75)Pr_(0.25)B₁₂ solid solution showing the presence ofzirconium and praseodymium in the dodecaboride phase. The praseodymiumrich areas correspond to PrB₆ (cubic, Pm3m structure, a=4.123 Å, ICSD615183), while the boron rich areas correspond to a higher boride phaseZrB₅₀ (rhombohedral, R3m structure, a=10.932 Å, c=23.849 Å). The thickhorizontal bars represent the intensity as a color legend.

FIG. 19 shows the SEM images and elemental maps for the hardestcompositions of the mixed metal dodecaborides: Zr_(0.5)Y_(0.5)B₁₂,Zr_(0.5)Sc_(0.5)B₁₂ and Y_(0.5)Sc_(0.5)B₁₂. For Zr_(0.5)Y_(0.5)B₁₂, bothZr and Y can be observed in the metal dodecaboride phase. In contrast,for the Sc containing dodecaboride solid solutions, Zr_(0.5)Sc_(0.5)B₁₂and Y_(0.5)Sc_(0.5)B₁₂, while Zr and Y can be seen primarily in thedodecaboride phase, Sc can be seen both in the dodecaboride phase aswell as in boron rich areas (as ScB₅₀). SEM images and elemental mapsfor boron (K line), scandium (K line), yttrium (L line), zirconium (Lline) for mixed metal dodecaboride solid-solutions: (top)Zr_(0.5)Y_(0.5)B₁₂, (middle) Zr_(0.5)Sc_(0.5)B₁₂, (bottom)Y_(0.5)Sc_(0.5)B₁₂. For Zr_(0.5)Y_(0.5)B₁₂ both zirconium and yttriumcan be observed in the metal dodecaboride phase. In contrast, for thescandium containing dodecaboride solid solutions, Zr_(0.5)Sc_(0.5)B₁₂and Y_(0.5)Sc_(0.5)B₁₂, while yttrium can be seen primarily in thedodecaboride phase, scandium can be seen both in dodecaboride phase aswell as in boron rich areas (as ScB₅₀). The thick horizontal barsrepresent the intensity as a color legend.

Example 7. Optical Microscopy

FIG. 20 shows the colors of solid solution samples of the mixed metaldodecaborides taken using an optical microscope. A color change of thedodecaboride phase can be directly observed using a light microscopegoing from pure ZrB₁₂ (violet) to YB₁₂ (light-blue) and ScB₁₂ (icebergblue) phase. The color change is most pronounced for theZr_(1-x)Y_(x)B₁₂ solid solution, which goes from violet for ZrB₁₂ tolight blue for YB₁₂. The color changes for Zr_(1-x)Sc_(x)B₁₂ andY_(1-x)Sc_(x)B₁₂ are less pronounced due to the similarities of theshades of blue of YB₁₂ and ScB₁₂.

The solid solution formation of the dodecaboride phase can be directlyobserved using a light microscope going from pure ZrB₁₂ (violet) toZr_(0.45)Gd_(0.55)B₁₂ (blue) and Zr_(0.70)Sm_(0.30)B₁₂ (blue-violet)shown in FIG. 21. The color change is due to the charge-transfer betweenthe cuboctahedron boron cage network and the metal atoms. It alsosuggests that pure GdB₁₂ and SmB₁₂ should be blue, similar to YB₁₂, asGd, Sm and Y are all in +3 oxidation states. The dark blue phaseobserved in Zr_(1-x)Sm_(x)B₁₂ is SmB₆.

Experimental

Zr_(1-x)Y_(x)B₁₂Zr_(1-y)Sc_(y)B₁₂ and Y_(1-y)Sc_(y)B₁₂

Mixed dodecaboride solid solutions, Zr_(1-x)Y_(x)B₁₂, (x=0.00, 0.05,0.25, 0.50, 0.75, 0.95 and 1.00), Zr_(1-y)Sc_(y)B₁₂, Y_(1-y)Sc_(y)B₁₂(y=0.00, 0.05, 0.25, 0.50, 0.75, 0.80, 0.85, 0.90, 0.95 and 1.00), ScB₅₀and YB₆₆ were synthesized using metal and boron powders of high-purity:amorphous boron (99+%, Strem Chemicals, U.S.A.), zirconium (99.5%, StremChemicals, U.S.A.), yttrium (99.9%, Strem Chemicals, U.S.A.) andscandium (99.9%, Sigma-Aldrich, U.S.A.). In order to prevent theformation of the lower boride phases, a metals to boron ratio of 1:20was used for the dodecaborides, 1:65 for ScB₅₀ and 1:70 for YB₆₆. Thepowders of boron and transition metals were weighed, homogenized in anagate mortar and pestle and pressed into pellets using a hydraulic press(Carver) under a 10 ton load. The samples were then arc-melted (I≥70amps, t=1-2 mins) in an ultra-high purity argon atmosphere.

Prepared ingots were bisected using a diamond saw (Ameritool Inc.,U.S.A.). One half was crushed into a sub 325 (45 μm) mesh powder andused for powder X-ray diffraction (PXRD) analysis; the other half wasused for energy-dispersive X-ray spectroscopy (EDS) analysis andVicker's hardness measurements. For the latter two, the samples wereencapsulated in epoxy using an epoxy/hardener set (Allied High TechProducts Inc., U.S.A.). In order to achieve an optically flat surface,the samples were polished on a semi-automated polisher (South BayTechnology Inc., U.S.A.), using the following abrasives: SiC discs of120-1200 grit sizes (Allied High Tech Products Inc., U.S.A.) and 30-1micron particle diamond films (South Bay Technology Inc., U.S.A.).

Powder XRD was carried out on a Bruker D8 Discover Powder X-rayDiffractometer (Bruker Corporation, Germany) utilizing Cu_(Kα) X-rayradiation (λ=1.5418 Å). The following scan parameters were used: 5-100°2θ range, time per step of 0.3 sec, step size of 0.0353° with a scanspeed of 0.1055°/sec. In order to determine the phases present in thepowder X-ray diffraction data, the Joint Committee on Powder DiffractionStandards (JCPDS) database was utilized. The composition and purity ofthe samples were determined on an FEI Nova 230 high resolution scanningelectron microscope (FEI Company, U.S.A.) with an UltraDry EDS detector(Thermo Scientific, U.S.A.). Transmission electron microscopy (TEM) wasperformed on a TF-20 transmission electron microscope in order toconfirm the crystal structure. Rietveld refinement utilizing Maudsoftware was carried out to determine the cell parameters. The hardnessof each sample was determined using a MicroMet 2103 Vickersmicrohardness tester (Buehler Ltd, U.S.A.). Fifteen indents of thefollowing force loading were made in random areas of the sample: 0.49,0.98, 1.96, 2.94 and 4.9 N (low to high, respectively). The length ofthe diagonals were measured using a high resolution optical microscope(Zeiss Axiotech 100HD, Carl Zeiss Vision GmbH, Germany) with 500×magnification, and Vickers hardness was calculated using the Equationbelow:

$H_{v} = \frac{1854.4F}{a^{2}}$where F is the loading force applied in Newtons (N) and a is the averageof the length of the two diagonals of each indent in micrometers.

Densities for the 50/50% solid solutions were calculated from powder XRDunit cell data and elemental composition from EDS.

Oxidation resistance was determined via thermogravimetric analysisutilizing a Pyris Diamond TGA/DTA unit (TG-DTA, Perkin-ElmerInstruments, U.S.A.). The following heating/cooling profile was used:heating in air from 25 to 200° C. (at 20° C./min), holding at 200° C.for 30 minutes, heating from 200 to 1000° C. (at 2° C./min), holding at1000° C. for 120 minutes, cooling 1000 to 25° C. (at 5° C./min).

To determine and establish the composition and phase purity of mixedMB₁₂ solid solutions, powder X-ray diffraction (PXRD) andenergy-dispersive X-ray spectroscopy (EDS) analyses were performed.FIGS. 1-3 show PXRD in the 5-100° 2 Θ for the three solid solutions:Zr_(1-x)Y_(x)B₁₂ (x=0.05, 0.25, 0.50, 0.75 and 0.95), Zr_(1-y)Sc_(y)B₁₂and Y_(1-y)Sc_(y)B₁₂ (y=0.05, 0.25, 0.50, 0.75, 0.80, 0.85, 0.90 and0.95). PXRD data for the β-rhombohedral boron doping phase of Sc (ScB₅₀,R3m) and YB₆₆ (Fm3c) (FIG. 16) compared to the reference patterns fromJCPDS (Joint Committee for Powder Diffraction Standards) can be seen inFIG. 24.

The three dodecaborides, ZrB₁₂, YB₁₂ and ScB₁₂, are completely solublein each other as binary metal substituted phases: Zr_(1-x)Y_(x)B₁₂,Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂. Samples with YB₁₂ contain YB₆₆as a minor phase, while ScB₁₂ samples contain ScBso (FIGS. 16 and 24).ZrB₁₂ and YB₁₂ form an essentially perfect solid solution (FIG. 15 andTable 1), which follows Vegard's Law within experimental error. This canbe attributed to the fact that both of these dodecaborides have thecubic-UB₁₂ (Fm3m) structure, the electronegativities of the metals aresimilar, and the differences in their radii are within the 15% set bythe Vegard's Law rules. On the other hand, ScB₁₂ possesses atetragonal-ScB₁₂ structure. This results in Zr_(1-x)Sc_(x)B₁₂ andY_(1-x)Sc_(x)B₁₂ solid solutions having a solid-state phase transitionat 90-95 at. % Sc (FIGS. 1-3 and Table 2-3). In addition,Zr_(1-x)Sc_(x)B₁₂ solid solutions were previously shown to undergo atemperature induced phase transition. Unit cell parameters for cubic(FCC) and body-centered tetragonal (BCT) syngonies as well as the phasecomposition as determined by EDS are presented in Tables 1-3. FIG. 19shows the SEM images and elemental maps for the hardest compositions ofthe mixed metal dodecaborides: Zr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂and Y_(0.5)Sc_(0.5)B₁₂. For Zr_(0.5)Y_(0.5)B₁₂, both Zr and Y can beobserved in the metal dodecaboride phase. In contrast, for the Sccontaining dodecaboride solid solutions, Zr_(0.5)Sc_(0.5)B₁₂ andY_(0.5)Sc_(0.5)B₁₂, while Zr and Y can be seen primarily in thedodecaboride phase, Sc can be seen both in the dodecaboride phase aswell as in boron rich areas (as ScB₅₀).

After establishing the purity of the samples, Vickers hardness testing(under a load of 0.49-4.9 N) was carried out, the results of which areshown in FIGS. 8-10. High covalent bond density of the dodecaborides maybe the reason that both pure MB₁₂ as well as their mixed metal solidsolutions are superhard (H_(v)≥40 GPa). For the Zr_(1-x)Y_(x)B₁₂ solidsolution, at the composition of Y=50 at. %, the hardness maximizes at45.8±1.3 GPa for a loading of 0.49 N, compared to 40.4±1.8 GPa for pureZrB₁₂ (compared to a literature value of 39 GPa) and 40.9±1.6 GPa forpure YB₁₂ (compared to a literature value of 42 GPa). We speculate thatthe 14% increase in hardness here is due to a combination of bothintrinsic factors (solid solution hardening) where incorporating atomsof different sizes (Zr: r_(at)=1.55 Å, r_(CN=12)=1.603 Å; Y: r_(at)=1.80Å, r_(CN=12)=1.801 Å) produces strain at a local scale and dislocationpropagation is therefore hindered; as well as extrinsic factors (due tosample morphology, microstructure and the presence of boron richphases). Zr_(1-x)Y_(x)B₁₂ solid solutions contain the YB₆₆ phase, whichin contrast to ScB₅₀, is not a β-rhombohedral boron doping phase, but aseparate Y—B phase. YB₆₆ (Fm3c, FIG. 16) contains 1584 boron atoms and24 Y atoms and is superhard (40.4±1.8 GPa at 0.49 N), potentiallyproviding some extrinsic hardening for these samples.

For the Zr_(1-x)Sc_(x)B₁₂ solid solution, the hardness increases to48.0±2.1 GPa at a composition of 50 at % Sc, compared to 40.4±1.8 GPafor pure ZrB₁₂ and 41.7±2.2 GPa for pure ScB₁₂. This hardness increasecan again be attributed to a combination of intrinsic (solid solutionhardening), since at this composition (Zr_(0.5)Sc_(0.5)B₁₂) ScB₁₂ isstabilized in the cubic structural type as well as extrinsic factors.The hardness of the solid solutions richer in Sc (x≥0.5) are harder thanthe corresponding samples richer in Zr (x≤0.5); this may be attributedto the fact that Zr_(1-x)Sc_(x)B₁₂ undergoes a cubic to tetragonal phasetransition at 90-95 at. % Sc. This is similar to the martensitictransformation in steel, where the unit cell transforms from a cubic toa body-centered tetragonal lattice through a diffusionlesstransformation. Solid solutions richer in Sc also contain the ScB₅₀phase (FIG. 16), which is a solid solution of Sc in β-rhombohedralboron. This phase, like most metal boron doping phases, is superhard(H_(v)≥40 GPa) at 42.1±2.2 GPa at 0.49 N, providing some extrinsichardening.

For the Y_(1-x)Sc_(x)B₁₂ solid solution, a hardness peak can be observedat 50 at. % Sc. The hardness increases to 45.2±2.1 GPa compared to40.9±1.6 GPa for pure YB₁₂ and 41.7±2.2 GPa for pure ScB₁₂. Similarly toZr_(1-x)Sc_(x)B₁₂, the hardness increase of Y_(1-x)Sc_(x)B₁₂ can beattributed to solid-solution hardening as well as the presence ofsecondary boron rich phase, ScB₅₀ phase, which is superhard (H_(v)≥40GPa at 0.5 N of applied loading). A cubic to tetragonal phase transitionoccurs at 90-95 at. % Sc for this solid solution.

In order to determine the cell parameters, Rietveld refinement wascarried out using Maud software (Tables 1-3). For Zr_(1-x)Y_(x)B₁₂ thelattice parameter (a) of the cubic cell changed from 7.412 Å for pureZrB₁₂ to 7.505 Å for pure YB₁₂ (FIGS. 1-3 and Table 1). The change andgradual increase of the cell parameters confirms that a solid solutionhas been formed. In order to check the composition of theZr_(1-x)Y_(x)B₁₂ phase, EDS analysis was performed (Table 1). Thisanalysis further confirmed the nearly perfect solid solution formationover all range of concentrations of Zr and Y in Zr_(1-x)Y_(x)B₁₂. Asboth of the parent dodecaborides (ZrB₁₂ and YB₁₂) are of the cubic-UB₁₂(Fm3m) structural type, this system has no solid-state phasetransformation.

For Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ solid solutions, not only cana change in the lattice parameters be observed indicative of theformation of a solid solution (Tables 2-3), but a solid state phasetransition between the cubic-UB₁₂ (Fm3m) and tetragonal-ScB₁₂ (I4/mmm)lattice types can be found as well. The phase transition occurs at˜90-95 at. % Sc for Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ solidsolutions. A face-centered-cubic (FCC) to body-centered tetragonal (BCT)transition can be imagined if two FCC unit cells are positioned suchthat they share a face. Thus, the shared face-centered positions of thecubic cells become the body-centered positions of the tetragonal cell;the cubic a lattice parameter then becomes the tetragonal c latticeparameter, while the tetragonal a lattice parameter is composed of thecubic face diagonals and equals the cubic parameter a times

$\frac{\sqrt{2}}{2}.$By refining the structural model to fit the data in the cubic andtetragonal unit cells over the whole range of solid solutions, we foundthat the values of the cubic a and tetragonal c lattice parameters stayessentially the same, within error, for low concentrations of scandiumand diverges as they approach pure ScB₁₂. Therefore, at smallconcentrations of a secondary metal (5-10 at. %), one can speculate thatthe structure of the resulting mixed dodecaboride with scandium keepsthe pure ScB₁₂ tetragonal unit cell, whereas with the addition of moresecondary metal, the unit cell stabilizes into the cubic-UB₁₂ structure.To provide evidence for this speculation, a TEM image of showing thetetragonal diffraction pattern for Zr_(0.05)Sc_(0.95)B₁₂ can be seen inFIGS. 22-23.

Analyzing the crystal structure of ZrB₁₂ (ICSD 23861), YB₁₂ (ICSD 23860)and ScB₁₂ (ICSD 68028), one observes that tetragonal-ScB₁₂ has shortermetal-B bonds, while having longer B—B bonds than other cubic metaldodecaborides. This leads to not only a distortion of the cuboctahedronboron cages, but also to stronger metal-boron bonds in tetragonal-ScB₁₂.Addition of a secondary transition metal in ScB₁₂ allows for thealleviation of the cuboctahedral distortion and as a consequencestabilizes M_(1-x)Sc_(x)B₁₂ solid solution in the cubic structural type.

Metal dodecaboride samples exhibit interesting colors, ranging fromviolet for ZrB₁₂ to light blue for YB₁₂ and iceberg blue for ScB₁₂. Thecolors are a result of charge-transfer from the metal atoms to thenetwork of boron cuboctahedron cages. FIG. 20 shows the colors of solidsolution samples of the mixed metal dodecaborides taken using an opticalmicroscope. The color change is most pronounced for the Zr_(1-x)Y_(x)B₁₂solid solution, which goes from violet for ZrB₁₂ to light blue for YB₁₂.The color changes for Zr_(1-x)Sc_(x)B₁₂ and Y_(1-x)Sc_(x)B₁₂ are lesspronounced due to the similarities of the shades of blue of YB₁₂ andScB₁₂.

Analysing the thermal stability data from TGA for the hardest solidsolutions of ZrB₁₂, YB₁₂ and ScB₁₂, one observes that the oxidationresistances for Zr_(0.5)Y_(0.5)B₁₂, Zr_(0.5)Sc_(0.5)B₁₂ andY_(0.5)Sc_(0.5)B₁₂ are comparable to their parent compounds (FIG. 12).Whereas, the oxidation resistances for ZrB₁₂, YB₁₂ and ScB₁₂ are ˜610°C., ˜715° C. and ˜685° C., respectively, the mixed dodecaboride solidsolutions are stable up until ˜630° C., ˜685° C. and ˜695° C.,respectively. This high oxidation resistance suggests that dodecaboridescould be a promising replacement for the current industrial standard,tungsten carbide, which oxidizes at ˜400° C. Furthermore, the densitiesfor the hardest compositions are low, owing to their high boron content.X-ray densities of Zr_(0.5)Y_(0.5)B₁₂ (3.52 g/cm³), Zr_(0.5)Sc_(0.5)B₁₂(3.32 g/cm³), and Y_(0.5)Sc_(0.5)B₁₂ (3.18 g/cm³) show that they are aslight, if not lighter than diamond (3.52 g/cm³). The low density,superhardness and enhanced oxidation resistance makes metaldodecaborides an interesting choice as potential materials for cuttingand machining or as lightweight protective coatings.

Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Pr_(x)B₁₂, andZr_(1-x)Nd_(x)B₁₂

Pellets of Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Pr_(x)B₁₂, andZr_(1-x)Nd_(x)B₁₂ (x=0.05, 0.25, 0.50, 0.75 and 0.95) were preparedusing high-purity metal and boron powders: amorphous boron (99+%, StremChemicals, USA), gadolinium (99%, Sigma-Aldrich, USA), zirconium (99.5%,Strem Chemicals, USA), samarium (Strem Chemicals, 99.9%), praseodymium(99.9%, Strem Chemicals, USA), and neodymium (99.8%, Strem Chemicals,USA). The metal to boron ratio was kept at a minimum of 1:20 to preventthe formation of lower borides (MB₆) as they are the ambient pressuremost stable boride phases of Gd, Sm, Nd, and Pr. The weighed mixtureswere homogenized in vials in a vortex mixer for ˜1 minute, thenconsolidated in a hydraulic press (Carver) under ˜10 tons before beingarc melted (I>70 amps, T=1-2 min) under a high purity argon atmosphere.

The resultant pellets were broken into 2-4 pieces by gently tappingusing a tool steel Plattner-style diamond crusher. Half of the pieceswere crushed using the aforementioned tool steel Plattner-style diamondcrusher to −325 mesh (≤45 μm) powder for powder XRD. PXRD was performedon a Bruker D8 Discover powder X-ray diffractometer (Bruker Corporation,Germany) utilizing a CuKα X-ray beam (λ=1.5418 Å) in the 5-100° 2θ rangewith a scan speed of 0.1055°/s, time per step of 0.3 s. The phasesanalyzed were cross-referenced against the Joint Committee on PowderDiffraction Standards (JCPDS) database. Maud software was used toperform the unit cell refinements.

One piece was encapsulated in an epoxy/hardener set (Allied High TechProducts Inc., USA) to be polished to an optically flat finish on asemi-automated polisher (Southbay Technology Inc., USA) using bothsilicon carbide abrasive disks of 120-1200 grit (Allied High TechProducts Inc., USA) and 30-1 μm particle-size diamond films (SouthbayTechnology Inc., USA).

The polished samples were analyzed using an UltraDry EDS detector(Thermo Scientific, USA) attached to an FEI Nova 230 high-resolutionscanning electron microscope (FEI Company, USA). Vickers hardnesstesting was performed using a MicroMet 2103 Vickers microhardness tester(Buehler Ltd., USA) with a pyramidal diamond indenter tip. 15 indentswere made at applied loadings of 0.49, 0.98, 1.96 each, and a minimum of10 indents were made at loadings of 2.94 and 4.9 N each, and wereperformed in random areas of the sample. A high resolution opticalmicroscope (Zeiss Axiotech 100HD, Carl Zeiss Vision GmbH, Germany) with500× magnification was used to measure the length of the diagonals ofeach indent. Vicker's hardness was calculated using the Equation below:

$H_{v} = \frac{1854.4F}{a^{2}}$

where F is the loading force applied in Newtons (N) and a is the averageof the length of the two diagonals of each indent in micrometers.

Thermogravimetric analysis utilizing a Pyris Diamond TGA/DTA unit(TG-DTA, Perkin-Elmer Instruments, U.S.A.) was used to determineoxidation resistance. The profile used for heating and cooling in airwas as follows: heat from 25 to 200° C. (at 20° C./min), hold at 200° C.for 30 minutes, heat from 200 to 1000° C. (at 2° C./min), hold at 1000°C. for 120 minutes, cool 1000 to 25° C. (at 5° C./min).

Phase determination and sample purity was determined using powder X-raydiffraction (PXRD) and energy-dispersive X-ray spectroscopy (EDS). PXRDdata (2 Θ=5-100°) for Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂,Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ solutions are shown in FIGS.4-7. EDS data for Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂,Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ (FIG. 18), hardness (FIG. 11)and thermogravimetric analysis (FIG. 13) data for Zr_(0.5)Gd_(0.5)B₁₂are discussed in detail later in this section. Unit cell parameters andcompositions for Zr_(1-x)Gd_(x)B₁₂, Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂and Zr_(1-x)Pr_(x)B₁₂ alloys are provided in Tables 4-7.

For Zr_(1-x)Gd_(x)B₁₂, the solubility limit of Gd in ZrB₁₂ is 54 at. %Gd, whereas for Zr_(1-x)Sm_(x)B₁₂, the solubility limit of Sm in ZrB₁₂is ˜15 at. % Sm. For Zr_(1-x)Nd_(x)B₁₂, the solubility limit of Nd inZrB₁₂ is ˜7 at. % Nd and for Zr_(1-x)Pr_(x)B₁₂, the solubility limit ofPr in ZrB₁₂ is 15 at. % Pr. The above solubilities were determined bypowder XRD and EDS analyses. Past the solubility limit of Gd, Sm, Nd andPr in ZrB₁₂, the amount of the respective hexaboride (MB₆) phases, whichare the highest stable borides, increase (FIGS. 4-7). As metaldodecaborides are typically formed along the tie line of anincongruently melting phase, they are accompanied by a lower boride (MB₂or MB₆) at metal to boron ratio of ˜1:12, and higher borides (MB₅₀ andMB₆₆) at larger metal to boron ratios 1:20. Cell parameters determinedfor each of the solid solution compositions as well as the metalcomposition for Zr_(1-x)Gd_(x)B₁₂ and Zr_(1-x)Sm_(x)B₁₂ are given inTables 4-5. Note that the solubility of the secondary metal (Sm—Pr) inZrB₁₂ decreases with increasing size of said metal, which is in goodagreement with the size requirements for the metal dodecaborideformation as discussed above.

Vickers hardness testing from 0.49 N (low load) to 4.9 N (high load) wasperformed on samples of Zr_(1-x)Gd_(x)B₁₂ (x=0.05, 0.25 and 0.50) afterthe composition and purity of each was established. The hardness ofZr_(1-x)Gd_(x)B₁₂ solid solutions did not change (within the measurementerror) remaining at around ˜40 GPa at 0.49 N, similar to the parentZrB₁₂ (40.4±1.8 GPa).

Elemental maps and SEM images of selected samples of Zr_(1-x)Gd_(x)B₁₂,Zr_(1-x)Sm_(x)B₁₂, Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ alloys(x=0.55, 0.30, 0.25 and 0.25 respectively) are presented in FIG. 18. Forthe Zr_(0.45)Gd_(0.55)B₁₂ solid solution, the presence of zirconium andgadolinium can be seen in the dodecaboride phase. The boron rich areascorrespond to a higher boride phase GdB₆₆ (cubic, Fm3c structure,a=23.449 Å, ICSD 614306). The Zr_(0.70)Sm_(0.30)B₁₂ solid solution showsthe presence of zirconium and samarium in the dodecaboride phase. Here,the samarium rich areas correspond to SmB₆ (cubic, Pm3m structure,a=4.133 Å, ICSD 194196), and the boron rich areas correspond to thehigher boride phase SmB₆₆ (cubic, Fm3c structure, a=23.468 Å). TheZr_(0.75)Nd_(0.25)B₁₂ and Zr_(0.75)Pr_(0.25)B₁₂ solid solutions show thepresence of both zirconium and the secondary metals, neodymium andpraseodymium, respectively, in the dodecaboride phase. The neodymiumrich areas correspond to NdB₆ (cubic, Pm3m structure, a=4.127 Å, ICSD614931), while the praseodymium rich areas correspond to PrB₆ (cubic,Pm3m structure, a=4.123 Å, ICSD 615183). In the samples containing Ndand Zr, the boron rich areas correspond to the higher boride phase NdB₆₆(cubic, Fm3c structure, a=23.476 Å) and ZrB₅₀ (rhombohedral, R3mstructure, a=10.932 Å, c=23.849 Å), respectively. For praseodymium,however, the metal rich areas correspond to PrB₆ (cubic, Pm3m structure,a=4.123 Å, ICSD 615183), while the boron rich areas correspond to thehigher boride phase ZrB₅₀ (rhombohedral, R3m structure, a=10.932 Å,c=23.849 Å) as the PrB₆₆ phase does not exist.

Maud software was used to perform the unit cell refinements. ForZr_(1-x)Gd_(x)B₁₂, the cubic unit cell parameter (a) reached a value of7.453 Å for the alloy with 55 nominal at. % Gd, compared to 7.412 Å and7.524 Å (value from high-pressure—6.5 GPa—synthesis) for pure ZrB₁₂ andGdB₁₂, respectively. The change in the unit cell suggests the formationof a solid solution between GdB₁₂ and ZrB₁₂. As more Gd is present inthe alloy, the GdB₆ phase concentration increases, as it is the ambientpressure stable boride phase.

EDS analysis and calculations using Vegard's Law were used to determinethe solubility limit of Gd in ZrB₁₂ (Table 4). Both methods gave a value54 at. % Gd in ZrB₁₂; the excess Gd formed the boron rich GdB₆₆ andZrB₅₀ phase. For Zr_(1-x)Sm_(x)B₁₂, the cubic unit cell parameter (a)reached a value of 7.428 Å for the alloy with 30 nominal at. % Sm,compared to 7.412 Å for pure ZrB₁₂. As the high pressure synthesis ofSmB₁₂ was not successful, since it likely requires a pressure in excessof 6.5 GPa, there is no literature value for its unit cell. However,using the composition from EDS analysis and unit cell refinements, theunit cell for pure SmB₁₂ can be determined through extrapolation 7.543Å. Still, the change in the unit cell suggests the formation of a solidsolution between SmB₁₂ and ZrB₁₂. As more Sm is present in the alloy,the SmB₆ phase concentration increases, as it is the ambient pressurestable boride phase for samarium.

For Zr_(1-x)Nd_(x)B₁₂ and Zr_(1-x)Pr_(x)B₁₂ there is a slight change inthe unit cell parameter (a) compared to the pure ZrB₁₂, corresponding tothe limited solubilities of Nd and Pr in ZrB₁₂, 7 and 4 at. %,respectively. Similar to SmB₁₂, the high-pressure synthesis of NdB₁₂ andPrB₁₂ was unsuccessful; therefore, it is not possible to compare theunit cells of the alloys with the unit cell of the pure compounds.

Another confirmation of the solid solution formation of the dodecaboridephase can be directly observed using a light microscope (FIG. 21) goingfrom pure ZrB₁₂ (violet) to Zr_(0.45)Gd_(0.55)B₁₂ (blue) andZr_(0.70)Sm_(0.30)B₁₂ (blue-violet). The color change is due to thecharge-transfer between the cuboctahedron boron cage network and themetal atoms. It also suggests that pure GdB₁₂ and SmB₁₂ should be blue,similar to YB₁₂, as Gd, Sm and Y are all in +3 oxidation states. Thedark blue phase observed in Zr_(1-x)Sm_(x)B₁₂ is SmB₆.

The thermal stability of the zirconium-gadolinium and zirconium-samariumborides was measured in air using thermogravimetric analysis (FIG. 13).The Zr_(0.5)Gd_(0.5)B₁₂ sample is stable in air up to ˜630° C., whileZr_(0.75) Sm_(0.25)B₁₂ up to ˜620° C. compared to ˜610° C. for pureZrB₁₂.

While preferred embodiments of the present disclosure have been shownand described herein, it will be obvious to those skilled in the artthat such embodiments are provided by way of example only. Numerousvariations, changes, and substitutions will now occur to those skilledin the art without departing from the disclosure. It should beunderstood that various alternatives to the embodiments of thedisclosure described herein may be employed in practicing thedisclosure. It is intended that the following claims define the scope ofthe disclosure and that methods and structures within the scope of theseclaims and their equivalents be covered thereby.

What is claimed is:
 1. A composite matrix comprising Zr_(1-x)Y_(x)B₁₂wherein x is from 0.001 to 0.999.
 2. A composite matrix comprisingZr_(1-x)Sc_(x)B₁₂ wherein x is from 0.001 to 0.999.
 3. A compositematrix comprising Y_(1-x)Sc_(x)B₁₂ wherein x is from 0.001 to 0.999. 4.A composite matrix comprising Zr_(1-x)Gd_(x)B₁₂ wherein x is from 0.001to 0.999.
 5. A composite matrix comprising Zr_(1-x)Sm_(x)B₁₂ wherein xis from 0.001 to 0.999.
 6. A composite matrix comprisingZr_(1-x)Nd_(x)B₁₂ wherein x is from 0.001 to 0.999.
 7. A compositematrix comprising Zr_(1-x)Pr_(x)B₁₂ wherein x is from 0.001 to 0.999.